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2023. 19(5). 502-509 Строительная механика инженерных конструкций и сооружений Structural Mechanics of Engineering Constructions and Buildings
HTTP://JOURNALS.RUDN.RU/STRUCTURAL-MECHANICS
DOI 10.22363/1815-5235-2023-19-5-502-509 UDC 69:502.131.1 EDN: HXKXDM
RESEARCH ARTICLE / НАУЧНАЯ СТАТЬЯ
Performance of reinforced concrete elements strengthened with carbon fiber CFRP at elevated temperatures
Hadeal H. Alzamili1 , Asser M. Elsheikh12 131
1 RUDN University, Moscow, Russian Federation
2 Mansoura University, Mansoura, Egypt E elsheykh_am@pfur.ru
Article history
Received: May 29, 2022 Revised: August 24, 2023 Accepted: August 28, 2023
Conflicts of interest
The authors declare that there is no conflict of interest.
Authors' contribution
Undivided co-authorship.
Abstract. The importance of the research topic is established by the problems that occur in structural buildings when exposed to fire accidents, where the concrete loses much part of its mechanical properties and therefore becomes out of service. Because reconstruction of damaged buildings has a high financial cost, it is necessary to focus on the restoration of damaged concrete members with performant techniques and proven efficiency in terms of increasing the strength of concrete and its resistance to high temperatures. The authors conduct a numerical investigation on the use of carbon fiber-reinforced polymer sheeting CFRP to restore various structural concrete elements such as beams, columns, and slabs damaged in fire accidents for two types of normal and high-strength concrete, in addition to studying the behavior of concrete after strengthening it with CFRP sheets. The results by showed that load capacity, stiffness index, and absorption energy index have been improved by using CFRP in comparison with undamaged and fire-damaged elements. Keywords: Beam, column, slab, carbon fiber, concrete
For citation
Alzamili H.H., Elsheikh A.M. Performance of reinforced concrete elements strengthened with carbon fiber CFRP at elevated temperatures. Structural Mechanics of Engineering Constructions and Buildings. 2023;19(5):502-509. http://doi.org/10.22363/ 1815-5235-2023-19-5-502-509
Alzamili Hadeal Hakim, PhD student, Department of Civil Engineering, Academy of Engineering, RUDN University, Moscow, Russian Federation; ORCID: 0000-0001-8109-3381; E-mail: HadealHakim8@gmail.com
Elsheikh Asser Mohamed, Assistant professor, Department of Civil Engineering, Academy of Engineering, RUDN University, Moscow, Russian Federation; Assistant professor, Department of Civil Engineering, Mansoura University, Mansoura, Egypt; ORCID: 0000-0002-1212-2924; E-mail: elsheykh_am@pfur.ru
© Alzamili H.H., Elsheikh A.M., 2023
(DCS) I ' ls work is licensed under a Creative Commons Attribution 4.0 International License https://creativecommons.Org/licenses/by-nc/4.0/legalcode
Характеристики железобетонных элементов,
усиленных углепластиком CFRP, при повышенных температурах
Х.Х. Альзамили1 , A.M. Эльшейх12 и
1 Российский университет дружбы народов, Москва, Российская Федерация
2 Мансура университет, Мансура, Египет И elsheykh_am@pfur.ru
История статьи
Поступила в редакцию: 29 мая 2023 г. Доработана: 24 августа 2023 г. Принята к публикации: 28 августа 2023 г.
Заявление о конфликте интересов
Авторы заявляют об отсутствии конфликта интересов.
Вклад авторов
Нераздельное соавторство.
Аннотация. Актуальность темы исследования обусловлена проблемами, возникающими в несущих зданиях при пожарах, когда бетон теряет большую часть своих механических свойств и, следовательно, выходит из строя. Поскольку реконструкция поврежденных зданий требует высоких финансовых затрат, необходимо сосредоточиться на восстановлении поврежденных бетонных элементов с использованием надежных методов и доказанной эффективности с точки зрения восстановления прочности бетона и повышения устойчивости к высоким температурам. В исследовании численно исследуется использование углепластика СРЯР, для восстановления различных структурных бетонных элементов, таких как балки, колонны и плиты, поврежденных в результате пожара, для двух типов нормального и высокопрочного бетона, а также изучается поведение бетона после укрепления его листами углепластика. Результаты показали, что несущая способность, индекс жесткости и индекс энергии поглощения были улучшены при использовании углепластика по сравнению с неповрежденными и поврежденными огнем элементами.
Ключевые слова: балка, колонна, плита, углепластик, бетон
Для цитирования
Alzamili H.H., Elsheikh A.M. Performance of reinforced concrete elements strengthened with carbon fiber CFRP at elevated temperatures // Строительная механика инженерных конструкций и сооружений. 2023. Т. 19. № 5. С. 502-509. http://doi.org/ 10.22363/1815-5235-2023-19-5-502-509
1. Introduction
Concrete is the most often used man-made material and the second most consumed substance in the world, next to water, due to its necessity for various construction applications and the long-term demand for them [1]. Concrete is a composite material comprised of various components, including aggregates, water, cement, and other cementitious elements as binder ingredients [2].
Concrete's preserved qualities after cooling from being subjected to high temperatures are typically referred to as residual properties. The period of exposure, the features, and the material composition of concrete can all have an impact on how these properties change significantly within the high temperature range associated with an exposed fire [3]. Compressive strength, tensile strength, elastic modulus, and stress-strain response are the principal mechanical parameters of concrete that are of interest after exposure to high temperatures. These characteristics are frequently used to evaluate how much strength concrete loses and degrades at high temperatures [4].
When heated to 300 °C, concrete loses around 25 % of its initial compressive strength, and when subjected to temperatures beyond 600 °C, it loses about 75 % [5; 6]. The tensile strength decreases in concrete with an increase in temperature [7]. The mechanical property of concrete that is commonly regarded as being most impacted by exposure to high temperatures is its modulus of elasticity. In comparison to compressive and tensile strength, the degradation of elastic modulus occurs much more quickly [8]. While considering the critical heating
Альзамили Хадиль Хаким, аспирант департамента строительства, инженерная академия, Российский университет дружбы народов, Москва, Российская Федерация; ORCID: 0000-0001-8109-3381; E-mail: HadealHakim8@gmail.com
Эльшейх Ассер Мохамед, кандидат технических наук, доцент департамента строительства, инженерная академия, Российский университет дружбы народов, Москва, Российская Федерация; доцент департамента строительства, Университет Мансуры, Мансура, Египет; ORCID: 00000002-1212-2924; E-mail: elsheykh_am@pfur.ru
level for residual mechanical strength characteristics of fiber-reinforced concrete, Eidan et al. [9] showed that, at 400 °C, the residual factors for fiber-reinforced concrete are often better than those of plain concrete.
At high temperatures under 1000 °C, the compressive strength significantly decreased, but steel fiber-reinforced concrete with a 1 % addition outperformed non-steel fiber-reinforced concrete [10]. Moghadam & Izadifard [11] compared the impact of steel fiber and glass fiber on the strength of concrete at high temperatures. While no chemical changes were observed at this temperature range, both for steel and glass fiber at tested temperatures up to 800 °C, they noticed that the compressive strength of normal, steel, and glass fiber concrete decreased as the temperature rose to 100 °C.
Fixing damaged concrete members frequently involves building an external reinforced concrete support or concrete jacket or epoxy-bonding metal plates for damaged component, among other methods [12]. Using a laminate made of fiber-reinforced composite materials, such as carbon and glass fiber-reinforced polymers, in place of the steel plates is a unique technology. In structural repairs and the restoration of reinforced concrete components, the use of high-performance fiber-reinforced cementitious composites has gained significance [13]. The CFRP has been extensively employed to strengthen various structural elements, such as beams, columns, and slabs, from the outside [14]. Due to the low weight, corrosion-resistance, and tensile strength of FRP materials, which were employed in the space industry in the 1970s, this application became quite popular. The RC columns are passively contained by the CFRP jacket, which is only stressed when a column is subjected to an additional axial force that produces dilatation. Several factors affect the degree of confinement and the overall improvement in strength of confined concrete columns' sizes, shapes, and fiber modulus, as well as their thickness and fiber rupture strain (circular, square, or rectangular) [15].
Several scholars, for example, Ashteyat et al. [16], Shehata et al. [17], and Mhanna et al. [18], have thoroughly studied carbon fiber-reinforced polymers. They investigated the effects of corner roundness, column height, cross-section form, layer count, and wrapping method (full or partial) on the strength and ductility of the RC column. They discovered that when the corner radius was rounded until it approached the circular section, and as the CFRP's thickness rose, the strength improved. When exposed to repeated loading, CFRP has the benefit of displaying a much higher tensile strength. They can also be easy to use on site without the need for specialized tools or labor and are highly resistant to corrosive effects due to the many properties of CFRP, including mechanical properties, spacing, dimensions, and configuration [16-18].
According to the previous analysis of the literature, it should be noted that while numerous studies have been conducted to examine the behavior of concrete members when exposed to fire, little is known about the behavior of these members when strengthened with CFRP. Hence, this study is devoted to the effectiveness of employing CFRP to repair damaged concrete elements.
2. Methodology
The obtained results from the numerical simulation for the beam, slab, and column under ambient temperatures, elevated temperatures, and, lastly, after strengthening the fire-damaged concrete element, will be included in this study. Each concrete element has two concrete strength types (normal 25 MPa and high 65 MPa), in addition to two thicknesses for CFRP. The simulations shall be divided into the referenced undamaged models, the fire-damaged models, and the strengthened models. ABAQUS offers a variety of material attributes that reflect how those materials behave under various simulations. The Poisson's ratio and the modulus of elasticity are two parameters that are frequently used to describe the elastic phase in isotropic materials. The concrete damaged plasticity model CDP is utilized in this study to characterize the concrete plastic phase because of its effectiveness in predicting the behavior of the concrete under a variety of conditions, including monolithic and repeated loadings, plain and reinforced concrete, and application, which depends on the material loading rate.
In this paper, the behavior of the various concrete elements under various thermal conditions and repair techniques will be presented and discussed in detail, showing the level of degradation and improvement in the elements' performance in terms of various flexural indices. Each concrete member category was designated according to the type of the element.
The concrete beam has a full-scale dimension of 5500 mm in length, 300 mm in width, and 500 mm in thickness, which is one of the three main concrete components that make up the majority of such constructions. The beam was strengthened with three steel bars, top and bottom, using 16 mm steel bars, stirrups along the length of the beam with consistent spacing using steel bars with a diameter of 10 mm each at 200 mm, and three
steel bars at the top and bottom using 16 mm steel bars. While for the concrete column element, the dimensions were selected to ensure that the column is classified as a short column, and the failure will occur due to concrete crushing.
The concrete column cross section dimensions are 300 mm by 400 mm and the length is 3000 mm; the longitudinal steel reinforcement was six bars with a diameter of 16 mm; and the transverse reinforcement (ties) was steel bars with a diameter of 10 mm and 200 mm spacing.
The slab's concrete proportions were also chosen to guarantee that its behavior qualifies as a two-way action slab. The slab's thickness was 200 mm, its aspect ratio was 1, and its dimensions were 5500 mm by 5500 mm. Two steel bar meshes (top and bottom) with a 12 mm diameter and a 200 mm spacing made up the embedded steel reinforcement.
Each member's concrete strength needs to be examined, as each type of concrete member shows a varied level of fire temperature decrease. The thermal destruction carried on by subjecting the faces of the concrete elements to the ISO-834 standards differs since there are four, three, and one subjected face in column, beam, and slab elements, respectively. The effects of high temperatures also differ depending on the type of concrete. The temperature starts to rise from the bottom of the exposed face [19].
3. CFRP material's characterization and modeling
In ABAQUS, the damage initiation criteria for fiber-reinforced composites are based on Hashin's theory (see Hashin and Rotem, 1973). The Hashin damage model predicts anisotropic damage in elastic-brittle materials [21]. It is primarily intended for use with fiber-reinforced composite materials and takes into account four different failure modes: fiber tension, fiber compression, matrix tension, and matrix compression [20]. Below are the equations for these failure modes (ABAQUS manual).
Fiber tensile failure criteria:
=1(a1>0). (1)
Fiber compressive failure criteria:
^=1K<0). (2)
Matrix tensile failure criteria:
(^i + i—)2 = 1(-2>0). (3)
Matrix compressive failure criteria:
a2 ^
2т23 и
+
2t23 и/
= (4)
2u vl12 u'
GC
where Gi is the stress in direction 1, 0\ut is the ultimate tensile stress in direction 1 (maximum tensile longitudinal strength), Gi uc is the ultimate compressive stress in direction 1 (maximum compressive longitudinal strength), G2 is the stress in direction 2, G2Ut is the ultimate tensile stress in direction 2 (maximum tensile transversal strength), G2UC is the ultimate compressive stress in direction 2 (maximum compressive transversal strength), G3 is the stress in 3 direction 3, T13 is the shear stress in plane 1-3, T23 is the shear stress in plane 2-3, t23U is the inter laminar ultimate shear strength in plane 2-3 (maximum shear strength in plane 2-3), T12 is the shear stress in plane 1-2, t 12U is the ultimate shear stress in plane 1-2 (maximum shear strength in plane 1-2).
Such a model requires defining the elastic properties matrix, such as the elastic and shear modulus for both directions (E1, E2, G11, G13, and G23), in addition to the longitudinal and transverse Poisson ratio of the
composite. The damage initiation can be defined by assigning the damage variables as listed in Table 1, they are the longitudinal and transverse values for tensile, compressive, and shear strength. In total, six parameters should be assigned to define the elastic properties in addition to six parameters to define the damage initiation response of the CFRP sheet.
Table 1
Elastic and failure parameters of used CFRP laminate [22]
Parameter Quantity
Elastic modulus of fabric, E1, E2, respectively 230 and 16.58GaPa
Longitudinal and transverse Poisson's ratio 0.30
Shear modulus G12, G13, G23, respectively 9188.5, 12259 and 5911 MPa
Longitudinal tensile and compressive strength 3900 and 3120 MPa
Transverse tensile and compressive strength 210.6 and 64.5 MPa
Longitudinal and transverse shear strength 210.6 and 276.9 MPa
In this study, the obtained results shall be presented in detail in the main part. This part includes the results of the numerical simulation after the verification process for the beam, slab, and column under different conditions, i.e., phase 1, under ambient temperatures; phase 2, under elevated temperatures, and finally, phase c, after strengthening of the fire damaged concrete element. The simulation works shall be divided into three phases or stages: Phase 1 for the referenced undamaged models, Phase 2 for the fire-damaged models, and finally Phase 3 for the strengthened models.
4. Analysis and Results
The indicators (ultimate load capacity, stiffness, ductility, and toughness) were tested at each of the three stages of work for all structural elements and for both types of concrete (NSC and HSC). The ultimate load capacity results of the reference and fired and after strengthening of normal and high strength concrete for three elements (beam, column, slab) are illustrated in Table 2. (R) refers to the reference undamaged concrete member, and (F) refers to the concrete member after exposure to fire.
Table 2
The effect of high temperature on ultimate load capacity
Ultimate load capacity
Structural member cases Column Beam Slab
NSC HSC NSC HSC NSC HSC
R 4783.3 8480 2521.2 4181.4 5941.6 10190.5
F 2582.6 7179.7 1236.8 2937.0 4143.7 8411.1
CFRP 1.5 3040 9676 1787.2 3666.8 5080.7 9599.9
CFRP 2.5 3826 10945 1975.8 4011.4 6405 11149.8
In HSC beams, the enhancement in stiffness is higher than the fire-damaged beam by about 150%. While an enhancement in stiffness was found to be approximately the same in terms of NSC beams, in the case of the stiffness index in slabs, neither the NSC slabs nor the HSC slabs succeed in recovering the initial stiffness, so it can be concluded that even with increasing the CFRP sheet layer thickness to 166 %, the stiffness was the same. For NSC columns, increasing CFRP layer thickness by 166 % resulted in increasing the level of performance by 130 %. While for the HSC column, increasing the CFRP layer thickness by 166 % resulted in increasing the level of performance by 175 %. For both of the concrete strength classes, the stiffness index results of the reference, fired, and post-strengthened elements (beam, column, slab) are illustrated in Table 3.
Table 3
The effect of high temperature on stiffness index
Stiffness index
Structural member cases Column Beam Slab
NSC HSC NSC HSC NSC HSC
R 790.67 1716.67 143.10 188.74 216.53 376.14
F 249.3 1188.46 54.85 98.39 115.42 300.75
CFRP 1.5 603 1798 56.36 155.61 115.87 299.65
CFRP 2.5 699 1922 69.08 140.94 116.74 300.36
CFRP has a greater impact on the ductility performance of the beam in normal-strength concrete beams than in the high-strength class. On the other hand, for high-strength concrete, a 166 % increase in the thickness of the CFRP layer resulted in an 188 % increase in column ductility. Compared to normal-strength concrete, which received no benefit from the increase, for both normal and high-strength concrete slabs, the 1.5 mm CFRP layer thickness had the same efficiency. Compared to the 2.5 mm thickness, which showed that the improvement in the normal strength was nearly 1.5 times greater than the high-strength slab. These findings regarding the ductility index on the CFRP-treated columns reveal that a notable improvement has been made with this treatment, and full recovery of the column's ductility has been achieved for both types of concrete strength. The ductility index results of the reference and fired and after strengthening of normal and high-strength concrete for three elements (beam, column, slab) are illustrated in Table 4.
Table 4
The effect of high temperature on ductility index
Ductility index
Structural member cases Column Beam Slab
NSC HSC NSC HSC NSC HSC
R 2.07 1.68 2.63 2.79 4.54 3.46
F 2.09 1.99 2.79 3.12 3.71 3.15
CFRP 1.5 3.13 4.20 3.69 3.02 3.65 3.20
CFRP 2.5 2.81 7.93 6.02 3.77 8.24 4.62
The CFRP-strengthened members have sufficiently improved for normal-strength concrete when compared to the fire-damaged beam type. Furthermore, in high-strength concrete, the improved beams' toughness was approximately 138 % and 117 %, respectively, higher than the reference undamaged beam. In terms of columns, the absorption energy has been recovered successfully for both types of concrete strengths. Moreover, for normal and high-strength concrete slabs, respectively, increasing the CFRP layer thickness by 166 % increased the slab's capacity for absorption energy by around 581 and 238 %, respectively. The absorption energy index results of the reference and fired and after strengthening of normal and high-strength concrete for three elements (beam, column, slab) are illustrated in Table 5.
Table 5
The effect of high temperature on absorption energy index
Absorption energy index
Structural member cases Column Beam Slab
NSC HSC NSC HSC NSC HSC
R 39.199 51.335 84.352 189.001 513.427 591.032
F 23.120 43.956 48.188 133.99 314.974 491.251
CFRP 1.5 51.318 118 166.444 261.718 278.399 509.853
CFRP 2.5 200.310 385 413.190 221.522 1617.729 1217.200
5. Conclusion
The use of CFRP as effective reinforcement and repair techniques for improving the characteristics of various reinforced concrete members both before and after exposure to high temperatures was discussed in this research. We draw the following conclusions from this study:
1. HSC fire damaged columns, confined with 1.5 and 2.5 mm of CFRP layer thickness, improved the load capacity significantly by about 134 and 152 %, respectively. While NSC Column, confined with 1.5 and 2.5 mm CFRP layer thickness resulted in improving the load capacity significantly by about 117 and 148 % respectively.
2. The load carrying capacities were enhanced by about 144 and 159 % for 1.5 mm and 2.5 mm CFRP strengthened NSC beams, respectively. The 1.5 and 2.5 mm CFRP strengthened HSC beams have reflected load capacities higher than the fire damaged beam by about 124 and 136 %, respectively.
3. It can be noticed that the load capacity has been recovered in the NSC slab by about 122 % and fully recovered by 154 % for the 1.5 and 2.5 mm CFRP thickness layers, respectively. While in HSC slabs, load capacity has been recovered to about 114 % and fully recovered to 132 % for 1.5 and 2.5 mm CFRP thickness layers.
References
1. Miliozzi A., Chieruzzi M., Torre L. Experimental investigation of a cementitious heat storage medium incorporating a solar salt/diatomite composite phase change material. Applied Energy. 2019;250:1023-1035. http://doi.org/10.1016/ j.apenergy.2019.05.090
2. Ni S., Gernay T. Predicting residual deformations in a reinforced concrete building structure after a fire event. Engineering Structures. 2020;202:109853. http://doi.org/10.1016/j.engstruct.2019.109853
3. Sharma N.K., Kumar P., Kumar S., Thomas B.S., Gupta R.C. Properties of concrete containing polished granite waste as partial substitution of coarse aggregate. Construction and Building Materials. 2017;151:158-163. http://doi.org/ 10.1016/j.conbuildmat.2017.06.081
4. Kodur V. Properties of concrete at elevated temperatures. ISRN Civil Engineering. 2014(2):1-15. http://doi.org/ 10.1155/2014/468510
5. Yonggui W., Shuaipeng L., Hughes P., Yuhui F. Mechanical properties and microstructure of basalt fibre and nano-silica reinforced recycled concrete after exposure to elevated temperatures. Construction and Building Materials. 2020;247(7): 118561. http ://doi.org/10.1016/j.conbuildmat.2020.118561
6. Xie J., Zhang Z., Lu Z., Sun M. Coupling effects of silica fume and steel-fiber on the compressive behaviour of recycled aggregate concrete after exposure to elevated temperature. Construction and Building Materials. 2018;184:752-764. http://doi.org/10.1016/j.conbuildmat.2018.07.035
7. Khaliq W., Waheed F. Mechanical response and spalling sensitivity of air entrained high-strength concrete at elevated temperatures. Construction and Building Materials. 2017;150:747-757. http://doi.org/10.1016/j.conbuildmat.2017. 06.039
8. Chen G.M., He Y.H., Yang H., Chen J.F., Guo Y.C. Compressive behavior of steel fiber reinforced recycled aggregate concrete after exposure to elevated temperatures. Construction and Building Materials. 2014;71:1-15. https:// doi.org/10.1016/j.conbuildmat.2014.08.012
9. Eidan J., Rasoolan I., Rezaeian A., Poorveis D. Residual mechanical properties of polypropylene fiber-reinforced concrete after heating. Construction and Building Materials. 2019;198:195-206. http://doi.org/10.1016/j.conbuildmat. 2018.11.209
10. Lau A., Anson M. Effect of high temperatures on high performance steel fibre reinforced concrete. Cement and concrete research. 2006;36(9):1698-1707. http://doi.org/10.1016/j.cemconres.2006.03.024
11. Moghadam M.A., Izadifard R.A. Effects of steel and glass fibers on mechanical and durability properties of concrete exposed to high temperatures. Fire Safety Journal. 2020;113(7):102978. http://doi.org/10.1016/j.firesaf.2020. 102978
12. Naqi A.W., Al-zuhairi A.H. Nonlinear Finite Element Analysis of RCMD Beams with Large Circular Opening Strengthened with CFRP Material. Journal of Engineering. 2020;26(11):170-183. http://doi.org/10.31026/j.eng.2020.11.11
13. Banerji S., Kodur V. Effect of temperature on mechanical properties of ultra-high performance concrete. Fire and Materials. 2022;46(1):287-301. http://doi.org/10.1002/fam.2979
14. Abadel A.A., Alharbi Y.R. Confinement effectiveness of CFRP strengthened ultra-high performance concrete cylinders exposed to elevated temperatures. Materials Science-Poland. 2021;39(4):478-490. http://doi.org/10.2478/ msp-2021-0040
15. Mazzotti C., Bilotta A., Carloni C., Ceroni F., D'Antino T., Nigro E., Pellegrino C. Bond between EBR FRP and concrete. Design Procedures for the Use of Composites in Strengthening of Reinforced Concrete Structures: 2016; State-of-
the-Art Report of the RILEM Technical Committee 234-DUC. Springer Publ.; 2016:39-96. http://doi.org/10.1007/978-94-017-7336-2_3
16. Ashteyat A.M., Obaidat Y.T., Al-Btoush A.Y., Hanandeh S. Experimental and numerical study of strengthening and repairing heat-damaged RC circular column using hybrid system of CFRP. Case Studies in Construction Materials. 2021;15(6):e00742. http://doi.org/10.1016/j.cscm.2021.e00742
17. Shehata I.A., Carneiro L.A., Shehata L.C. Strength of short concrete columns confined with CFRP sheets. Materials and structures. 2002;35:50-58. http://doi.org/10.1617/13686
18. Mhanna H.H., Hawileh R.A., Abdalla J. A. Shear strengthening of reinforced concrete beams using CFRP wraps. Procedia Structural Integrity, 2019;17:214-221. http://doi.org/10.1016/j.prostr.2019.08.029
19. Elsheikh A., Alzamili H.H. Post Fire Behavior of Structural Reinforced Concrete Member (Slab) Repairing with Various Materials. Civil Engineering Journal. 2023;9(8):2012-2031. http://doi.org/10.28991/CEJ-2023-09-08-013
20. Hashin Z. Failure criteria for unidirectional fiber composites. Journal of Applied Mechanics. 1980;47(2):329-334. https://doi.org/10.1115/L3153664
21. Hashin Z., Rotem A. A fatigue failure criterion for fiber reinforced materials. Journal of Composite Materials. 1973;7(4):448-64. http://doi.org/10.1177/002199837300700404
22. Hochard C., Aubourg P.A., Charles J.P. Modelling of the mechanical behaviour of woven-fabric CFRP laminates up to failure. Composites science and technology. 2001;61(2):221-230.
