Methodology for the elaboration of the design table of GFRP structures subjected to fire

Methodology for the elaboration of the design table of GFRP structures subjected to fire Harkaitz García1*, Mikel Zubizarreta2 and Iñaki Garmendia1 1Mechanical Engineering Department, Faculty of Engineering Gipuzkoa, University of the Basque Country UPV/EHU, Plaza de Europa, 1 20018) Donostia-San Sebastián, Spain *arkaitz.garci[email protected]us 2Bussines Organization Department, Faculty of Engineering Gipuzkoa, University of the Basque Country UPV/EHU, Plaza de Europa, 1 20018) Donostia-San Sebastián, Spain “This is an accepted manuscript of an article published by Taylor & Francis in Mechanics of Advanced Materials and Structures on 16 October 2021, available at: https://doi.org/10.1080/15376494.2021.1980924.” “This is an Accepted Manuscript version of the following article, accepted for publication in Mechanics of Advanced Materials and Structures. H. García, M. Zubizarreta & I. Garmendia (2022) Methodology for the elaboration of the design table of GFRP structures subjected to fire, Mechanics of Advanced Materials and Structures, 29:27, 6495-6504, DOI: 10.1080/15376494.2021.1980924 . It is deposited under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/ licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.” ARTICLE TEMPLATE Methodology for the elaboration of the design table of GFRP structures subjected to fire H. Garc´ıaa, M. Zubizarretaband I. Garmendiaa aMechanical Engineering Department, Faculty of Engineering Gipuzkoa, University of the Basque Country UPV/EHU, Plaza de Europa, 1 20018) Donostia-San Sebasti´an, Spain; bBussines Organization Department, Faculty of Engineering Gipuzkoa, University of the Basque Country UPV/EHU, Plaza de Europa, 1 20018) Donostia-San Sebasti´an, Spain ARTICLE HISTORY Compiled September 1, 2021 ABSTRACT The main objective of this study is to establish a fire protection design method for pultruded Glass Fiber Reinforced Polymer (GFRP) structures exposed to fire. The method is based on the development of tables similar to those already available for steel structures. The structural designer may use these tables to determine the minimum required thickness (of any type of insulation), so that the structure maintains its mechanical properties above the over-dimensioning coefficient. The method used to draw up these tables follows four steps; i) First, the limit temperatures are determined or the temperature ranges within which the application of pultruded GFRP is permitted; ii) Second, the behavior of certain physical properties (density, specific heat, thermal conductivity, emissivity...) are defined as a function of the temperature; iii) Third, the method to determine the fire resistance temperature of the pultruded profile sections is defined; iv) Finally, the mechanical properties and ultimate resistance values of these profiles at different temperatures are also estimated. The behavior of the mechanical properties is analyzed as a function of the massivity of each section and the ratio between the thermal conductivity of the insulation and its thickness. In addition, a practical example is given of the application of the tables to a pultruded GFRP structure. KEYWORDS Pultruded elements; Fire protection; dimensioning method 1. Introduction One main limitation of pultruded Glass Fiber Reinforced Polymer (GFRP) profiles in building and bridge structures is their poor performance when exposed to fire Wong, Davies, and Wang (2004); Rosa et al. (2018, 2019). The authors of this paper nevertheless believe that there should be some rules or standards for its design, as is indeed the case of other structural materials. Among the characteristics of pultruded GFRP profiles is that most of them should be classified as class 4 sections, as in Eurocode 3, if analyzed in a similar way to steel CEN (2005). At room temperature, Class 4 sections have different and more complex characteristics than Class 1, 2 and 3 sections, mainly due to the likelihood of local buckling within CONTACT H. Garc´ıa. Email: [email protected] the section. A behavior that necessitates specific design rules and their corresponding design methods, which are already well established in the case of steel CEN (2005). Design methods are likewise under development for pultruded components Ascione et al. (2016). At higher temperatures (fire situations), Class 4 steel sections are usually oversized in most buildings Couto et al. (2016); Knobloch et al. (2012); Couto et al. (2018); Maia et al. (2016), due to the fact that, in practice, they are limited to the critical temperature of 350ºC CEN (2005), when, in reality, they could continue to work at higher temperatures Franssen, Zhao, and Gernay (2016); Jandera, Prachaˇr, and Wald (2020); Prachar et al. (2015). Up until now, different countries have had their own design guidelines for Fiber Reinforced Polymer (FRP) structures, i.e., Germany BUE (2010), Italy Council et al. (2007), the Netherlands CUR Commission C124 (2003) and the United States Association et al. (2012). No specific procedures have been proposed for design at elevated temperatures in these guidelines, while design rules are available for steel Eurocode (1993), concrete del Hormig´on Estructural (2008) and wood for Standardization (CEN). Moreover, there are no specific fire protection design procedures in the draft versions of the future Eurocode for FRP Ascione et al. (2016). This future standard needs to make a contribution in this respect Maraveas, Miamis, and Vrakas (2012) In this study, a design method is proposed for pultruded GFRP components. A table is presented to obtain the minimum insulation thickness necessary to achieve the mechanical properties required for each section of the structure. The tables were calculated for fire resistance times of less than 60 minutes. While investigating these values, it was concluded that longer exposure times were not viable for coatings of reasonable thickness. The tables were therefore not limited to the standard intervals of 30, 60, and 90 minutes. Instead, they were organized into shorter periods, from 5 to 60 minutes, in 5-minute increments. The discretization of time periods can be useful for optimization of the fire design of structures, although it requires specific calculations and the adjustment of the ”requested standard times”. The equivalent time equation is one suggested method that could be used Eurocode (2002). 2. Methodology The steps taken to obtain the tables presented in the design method proposed in this article are explained below (Figure 1): The symbols used in this article are presented below: •Tg:glass transition •Td:decomposition temperature •Em: modulus of elasticity •Eg: glassy modulus •Er: rubbery modulus •αg :conversion degree of the glass transition •ρ:density •cp: specific heat •: emissivity •λ: thermal conductivity •d: coating thickness 2 Limit temperatures Tg and Td for GFRP material Step 1Available Guides research in scientific articles Behavior of the physical properties of the GFRP (ρ, cp, ε...) up to Td Step 2 research in scientific articles Equation of temperature of protected sections Step 3Eurocode 3 + FEM + TLP Equations of mechanical properties at different temperatures Step 4research in scientific articles Table for the design of FRP elements at elevated temperatures Step 5 Figure 1. Methodology for the development of the table 3 •λp: effective thermal conductivity of the coating 2.1. Step 1: Limit temperatures for pultruded GFRP material. In this first step, our aim was to determine the temperature range in which the pultruded GFRP material may be used in structures. To do so, a bibliographical search of articles and existing guides was performed. Bai et al. Bai and Keller (2007) stated that the elastic Young’s modulus underwent a considerable (although recoverable) decrease during its glass transition at Tg temperature. They also stated that, although the moduli of longitudinal and transverse elasticity were different in this type of material, the decrease was similar for values between the glass transition temperature, Tg and the decomposition temperature, Td Bai et al. (2008). These reasons explain why the existing guidelines limit the use of GFRP to temperatures close to Tg. Taking the data of common pultruded GFRP material used in the work of Morgado et al. Morgado et al. (2018); Morgado, Silvestre, and Correia (2018a,b) (Tg=141ºC, Td=370ºC) as a reference, the limit temperatures of some guides might be as follows: •ASCE Association et al. (2012): Tg-22 = 141 – 22= 119 ºC •German guideline BUE (2010): Tg-15 = 141 – 15= 126 ºC •Dutch CUR Commission C124 (2003): Tg-20 = 141 – 20= 121 ºC Using a mean Tg ≃120ºC In the specific design procedure for pultruded GFRP structures discussed in this article, three design ranges are proposed depending on the temperature of the section: •Zone 1 (white): θ < 120ºC •Zone 2 (light grey): 120ºC≤θ≤370ºC •Zone 3 (dark grey): θ > 370ºC In Zone 1 it is possible to calculate the structures without modifying their elastic moduli. In Zone 2 the elastic moduli should be corrected using those values corresponding to the real temperature of the section. the equation presented by Bai et al. Bai, Keller, and Vall´ee (2008) (1) is proposed to obtain the modulus of elasticity. Finally, it is not advisable to design pultruded GFRP structures within the range corresponding to Zone 3. Em=Eg·(1 −αg) + Er·αg·(1 −αg) (1) where, Em is the modulus of elasticity, Eg and Er are the glassy and rubbery modulus, respectively, and αg·is the conversion degree of the glass transition. Figure 2 shows the three zones for different section sizes. 2.2. Step 2: Behavior of the physical properties of pultruded GFRP material. In Step 2, a bibliographic search was conducted for data that reflect the behavior of the material properties as a function of the temperature: density ρ, specific heat cp, emissivity and thermal conductivity λ, of the pultruded GFRP materials up to the limit temperatures obtained in Step 1. 4 50 m¯ ¹ 200 m¯ ¹ d/λp 5 10 15 20 25 30 35 40 45 50 55 60 d/λp 5 10 15 20 25 30 35 40 45 50 55 60 0.05 338 512 613 673 708 732 757 802 855 891 917 936 0.05 557 709 783 880 923 946 960 970 977 983 987 992 0.1 185 347 453 529 586 630 663 688 706 720 734 748 0.1 319 541 653 710 748 800 854 891 917 936 951 962 0.15 98 237 342 420 480 530 571 605 633 657 676 691 0.15 124 362 504 596 658 699 727 753 786 825 856 880 0.2 50 154 252 330 393 444 487 525 557 585 610 631 0.2 34 188 347 457 537 598 645 680 706 727 746 767 0.25 34 92 177 252 315 368 413 452 486 516 543 567 0.25 34 56 187 309 402 475 533 581 620 653 680 701 0.3 34 53 116 185 246 299 345 385 421 452 480 506 0.3 34 34 60 158 257 341 409 465 513 554 589 619 0.35 34 35 71 127 183 235 281 322 359 391 421 447 0.35 34 34 34 48 116 198 273 337 393 441 482 519 0.4 34 34 43 81 129 177 221 262 299 333 363 391 0.4 34 34 34 34 36 73 134 199 260 315 363 406 0.45 34 34 34 50 84 125 167 206 243 277 308 336 0.45 34 34 34 34 34 34 41 76 126 180 231 279 0.5 34 34 34 36 53 83 118 155 190 223 254 283 0.5 34 34 34 34 34 34 34 34 39 65 103 146 0.55 34 34 34 34 37 53 79 109 141 172 203 231 0.55 34 34 34 34 34 34 34 34 34 34 35 48 0.6 34 34 34 34 34 37 51 73 99 127 155 182 0.6 34 34 34 34 34 34 34 34 34 34 34 34 100 m¯ ¹ 250 m¯ ¹ d/λp 5 10 15 20 25 30 35 40 45 50 55 60 d/λp 5 10 15 20 25 30 35 40 45 50 55 60 0.05 450 629 705 746 812 879 917 941 957 969 977 984 0.05 588 728 832 904 935 953 964 972 978 984 988 992 0.1 254 450 564 638 685 714 737 761 802 846 878 903 0.1 335 564 674 727 774 838 882 911 932 948 960 970 0.15 121 310 433 519 583 632 668 694 713 729 745 764 0.15 114 370 519 613 675 714 743 777 818 851 877 898 0.2 47 190 316 409 480 536 582 619 649 674 693 708 0.2 34 171 343 461 545 608 656 692 718 740 763 790 0.25 34 95 208 304 381 442 492 535 571 603 629 652 0.25 34 39 158 290 392 471 533 584 625 660 687 709 0.3 34 41 116 205 284 349 404 450 490 525 556 583 0.3 34 34 37 116 222 313 389 451 503 547 585 618 0.35 34 34 53 118 191 257 315 365 409 447 480 511 0.35 34 34 34 34 68 145 225 298 360 414 460 501 0.4 34 34 34 56 110 170 227 279 325 366 403 436 0.4 34 34 34 34 34 37 73 134 199 259 314 363 0.45 34 34 34 34 53 95 145 195 242 285 324 359 0.45 34 34 34 34 34 34 34 35 58 102 153 205 0.5 34 34 34 34 34 46 78 118 161 203 243 280 0.5 34 34 34 34 34 34 34 34 34 34 39 63 0.55 34 34 34 34 34 34 39 60 92 128 165 201 0.55 34 34 34 34 34 34 34 34 34 34 34 34 0.6 34 34 34 34 34 34 34 35 46 68 96 128 0.6 34 34 34 34 34 34 34 34 34 34 34 34 150 m¯ ¹ 300 m¯ ¹ d/λp 5 10 15 20 25 30 35 40 45 50 55 60 d/λp 5 10 15 20 25 30 35 40 45 50 55 60 0.05 514 682 742 829 895 930 950 963 973 980 985 990 0.05 611 743 860 916 941 956 966 973 979 985 989 993 0.1 294 506 620 686 722 753 799 850 886 912 931 946 0.1 345 581 689 741 802 860 897 922 941 954 965 973 0.15 128 345 478 568 632 676 706 728 749 776 812 844 0.15 100 371 526 623 686 724 757 798 836 866 889 908 0.2 39 196 341 443 518 577 623 659 687 708 725 741 0.2 34 148 331 457 546 612 662 699 725 749 776 805 0.25 34 78 206 316 401 468 523 568 606 637 664 685 0.25 34 34 123 263 374 459 526 580 624 660 690 713 0.3 34 34 91 190 280 355 416 468 512 549 582 611 0.3 34 34 34 74 176 276 359 428 485 533 574 609 0.35 34 34 35 84 162 238 305 362 411 454 492 525 0.35 34 34 34 34 37 88 167 246 315 376 428 473 0.4 34 34 34 35 67 126 191 251 305 352 395 432 0.4 34 34 34 34 34 34 36 69 126 190 250 306 0.45 34 34 34 34 34 49 90 142 195 245 291 332 0.45 34 34 34 34 34 34 34 34 34 41 73 119 0.5 34 34 34 34 34 34 36 58 95 139 183 226 0.5 34 34 34 34 34 34 34 34 34 34 34 34 0.55 34 34 34 34 34 34 34 34 38 58 88 124 0.55 34 34 34 34 34 34 34 34 34 34 34 34 0.6 34 34 34 34 34 34 34 34 34 34 36 50 0.6 34 34 34 34 34 34 34 34 34 34 34 34 time (min) time (min) time (min) time (min) time (min) time (min) Figure 2. Design tables, zones 1, 2 and 3 for different section sizes 5 According to Correia et al. Correia, Bai, and Keller (2015), the thermo-physical properties (density, specific heat and thermal conductivity) remain stable until the decomposition temperature of the material (Td). However, Bai et al. proposed equations as a function of temperature that define the behavior of the thermal conductivity λBai et al. (2008), the specific heat ratio and the density Yu, Till, and Thomas (2007). Although Keller et al. also analyzed and proposed a linear progression for the emissivity coefficient Keller, Tracy, and Zhou (2006), it was decided to use the equations of Bai et al. to obtain the tables presented in this article. 2.3. Step 3: Temperature calculation for pultruded GFRP beams exposed to fire. Eurocode 3, parts 1-2 is only applicable to steel structures exposed to fire Eurocode (1993). The formulae that appear in that context are therefore limited to these metal components. However, it appears highly desirable to have a set of equivalent formulae that could be used for pultruded GFRP beams and columns. The method followed to develop such a set of formulae was to investigate the basic assumptions of the EC-3 norm, in order to establish whether they are applicable to the case of pultruded GFRP. 2.3.1. Assumptions for steel sections The main assumption of the EC-3 norm is that, if the exposure and the insulation are equal on all exposed surfaces, then the temperature of an insulated steel structure exposed to fire may be estimated by a one-dimensional analysis. At the same time, the corner effects are neglected. In addition, as the thermal diffusivity of steel is very high, it can be assumed that the heat will be uniformly distributed throughout the steel Wickstr¨om (1985). An HEB-300 steel section was used as a case study to verify these assumptions. The steel section was insulated with a 25 mm rock wool layer. Three different numerical methods were used to calculate the temperatures distribution over time: the TLP (Thermal Lumped Parameter) method Associates (2019); Garmendia et al. (2016), the formula (4.27) from EC-3 Eurocode (1993) and the well-established Finite Element Method. The temperature of the fire was taken from the ISO 834 curve Standard (1999), as shown in (2): θg= 20 + 345 ·log (8t+ 1) (2) where, t is expressed in minutes and θg in ºC. The first method, the TLP method, assumes a two-node network model (gas node number 1 and steel node number 2) with a single linear conductance between both (GL(1,2)=0.71120 W/ºC). This linear conductance is the inverse value of the thermal resistance that is present due to the insulation layer. The steel is assumed to have a single temperature (at node 2) with a thermal inertia of M2C2=16817.055 J/ºC. The temperature at node 1 is imposed as a boundary condition and as a function of time. The program (called TK) calculates temperature at node 2 as a function of time, producing a numerical solution to the differential equation (3): 6 GL (1,2) (T1−T2) + M2C2 dT2 dt = 0 (3) The second method integrates the equation in EuroCode-3 CEN (2005) over time (4): ∆θa,t =λpAp/V (θg,t −θa,t) dpcaρa(1 + φ/3) ∆t−eφ/10 −1∆θg,t (4) following the method suggested in Franssen, Kodur, and Zaharia (2009). Finally, the Finite Element Method was used to model a quarter of the HEB section, which is sufficient due to geometry and loads symmetries. The mesh shown in Figure 3 was used where the different materials (steel and insulation) are color coded. The results of the three methods are summarized below in Figure 4. The results of the three methods compare well. For the FEM method, a temperature distribution on the section (differences lower than 12 ºC, see Figure 5) was calculated with the FEM method and a mean temperature value was used for the comparisons. From these results, it is possible to state that the three methods could be used to estimate the steel temperature and that the assumption of a single temperature representing the thermal state of the steel is appropriate. 2.3.2. Assumptions for pultruded GFRP material The idea is now to use the three previously mentioned methods to estimate the GFRP temperature as a function of time, so as to evaluate whether the assumption of a single temperature that represents the thermal state of the GFRP is appropriate. Pultruded GFRP material properties were used as a function of the temperature, obtained from the prospect for new guidance Ascione et al. (2016). The results are summarized in Figure 6. Reasonable comparisons between the three curves were evident with temperature values that were higher than those assumed for the steel section. The pultruded GFRP section presented quite large gradients, as can be seen in Figure 7. The mean value of the FEM results reflected in Figure 6 provided a reasonable representation of the thermal state of the whole pultruded GFRP section. However, if the maximum temperature in the section is analyzed, it is far off the mean value (those calculated with any of the three methods); a difference that was larger as the exposure time increased. 2.3.3. Relation between TEC-3 and Tmax FEM The thermal conductivity of pultruded GFRP is much lower than steel. This fact results in differences between the maximum and the mean temperatures of the GFRP sections. This difference is more evident for sections with the fewest faces exposed to fire where the low conductivity of GFRP plays an important role. The fewer the number of faces exposed to fire, the larger the difference between the maximum temperature within the section and that obtained with eq. (4). The number of different cases that can be devised with different section geometries and the number of faces exposed to fire is extremely high. As a consequence, it was 7 Figure 3. Mesh and materials of a HEB-300 case study 8 d/λ=0.4  d= 0.08m I-BEAM 152X76X10  Massivity 200 m-1  RF 30 min d/λ=0.35  d=0.07m Figure 10. Application of the table for practical example 15 Some real cases of GFRP structures are presented in Figure 11. 5. Conclusions •Having developed the fire design table and after searching for all tests performed to date, an important conclusion was that with the most common insulation thicknesses available for the type of application, GFRP + insulation sections cannot maintain their mechanical properties for exposure times longer than 60 minutes. •If the temperature section remains between the glass transition, Tg, and the decomposition temperature, Td (Zone 2), the structure will probably be valid, but the modulus of elasticity of the section must be corrected (1). •In contrast with the steel sections, the temperature within the GFRP section cannot be considered constant (due to its much lower thermal conductivity). A corrector equation (eq. 5) is proposed for GFRP sections exposed from the four sides, in order to obtain the maximum section temperature. •After the calculation or dimensioning for a persistent situation and with the oversizing coefficients for the extraordinary fire situation, it is a straightforward task to obtain the necessary insulation thicknesses using the design table that has been proposed in this study. 6. References References 2010. “Structural polymer components for building and construction. Draft, dimensioning and construction.” . Ascione, L, JF Caron, P Godonou, K Van IJselmuijden, J Knippers, T Mottram, M Oppe, M Gantriis Sorensen, J Taby, and L Tromp. 2016. “Prospect for new guidance in the design of FRP.” Support to the implementation, harmonization and future development of the Eurocodes. JRC Report EUR 27666. Associates, k. 2019. “http://www.tak2000.com/data/handbookx.pdf.” USA. Association, American Composites Manufactures, et al. 2012. “Pre-standard for load & resistance factor design (LRFD) of pultruded fiber reinforced polymer (FRP) structures.” Arlington, VA: ACMA 14. Bai, Yu, and Thomas Keller. 2007. “Modeling of post-fire stiffness of E-glass fiber-reinforced polyester composites.” Composites Part A: applied science and manufacturing 38 (10): 2142– 2153. Bai, Yu, Thomas Keller, and Till Vall´ee. 2008. “Modeling of stiffness of FRP composites under elevated and high temperatures.” Composites Science and Technology 68 (15-16): 3099–3106. Bai, Yu, Nathan L Post, John J Lesko, and Thomas Keller. 2008. “Experimental investigations on temperature-dependent thermo-physical and mechanical properties of pultruded GFRP composites.” Thermochimica Acta 469 (1-2): 28–35. CEN, EN. 2005. “1-1-Eurocode 3: Design of steel structures-Part 1-1: General rules and rules for buildings.” European Committee for Standardization, Brussels . Correia, Jo˜ao R, Yu Bai, and Thomas Keller. 2015. “A review of the fire behaviour of pultruded GFRP structural profiles for civil engineering applications.” Composite Structures 127: 267– 287. Correia, Jo˜ao R, Marco M Gomes, Jos´e M Pires, and Fernando A Branco. 2013. “Mechanical 16 Figure 11. Some real cases of GFRP structures 17 behaviour of pultruded glass fibre reinforced polymer composites at elevated temperature: Experiments and model assessment.” Composite Structures 98: 303–313. Council, National Research, et al. 2007. “Guide for the Design and Construction of Structures made of FRP Pultruded Elements.” CNR-DT 205: 25–31. Couto, Carlos, ´ Elio Maia, Paulo Vila Real, and Nuno Lopes. 2018. “The effect of non-uniform bending on the lateral stability of steel beams with slender cross-section at elevated temperatures.” Engineering Structures 163: 153–166. Couto, Carlos, Paulo Vila Real, Nuno Lopes, and Bin Zhao. 2016. “Local buckling in laterally restrained steel beam-columns in case of fire.” Journal of Constructional Steel Research 122: 543–556. CUR Commission C124, The Netherlands, Gouda. 2003. “Fibre-Reinforced Polymers in Civil Load-Bearing Structures.” . del Hormig´on Estructural, Instrucci´on. 2008. “EHE-08.” Madrid, Ministerio de Fomento, Secretar´ıa General T´ecnica . Eurocode, EC. 1993. “3: Design of steel structures: Part 1.2, general rules–structural fire design.” Brussels: European Committee for Standardization. DD ENV 1 (2). Eurocode, EC. 2002. “1: Actions on structures: Part 1.2, General actions-Actions on structu res exposed to fi re.” Brussels: European Committee for Standardization . for Standardization (CEN), European Committee. 2004. “Eurocode 5—Design of timber structures, Part 1–2: General—Structural fire design.” . Franssen, Jean Marc, Venkatesh Kodur, and Raul Zaharia. 2009. Designing steel structures for fire safety. CRc Press. Franssen, Jean-Marc, Bin Zhao, and Thomas Gernay. 2016. “Experimental tests and numerical modelling on slender steel columns at high temperatures.” Journal of Structural Fire Engineering 7 (1): 30–40. Garmendia, I˜naki, Eva Anglada, Haritz Vallejo, and Miguel Seco. 2016. “Accurate calculation of conductive conductances in complex geometries for spacecrafts thermal models.” Advances in Space Research 57 (4): 1087–1097. Jandera, Michal, Martin Prachaˇr, and Frantiˇsek Wald. 2020. “Lateral-torsional buckling of class 4 section uniform and web tapered beams at elevated temperature.” Thin-Walled Structures 146: 106458. Keller, Thomas, Craig Tracy, and Aixi Zhou. 2006. “Structural response of liquid-cooled GFRP slabs subjected to fire–Part II: Thermo-chemical and thermo-mechanical modeling.” Composites Part A: applied science and manufacturing 37 (9): 1296–1308. Knobloch, Markus, Diego Somaini, Jacqueline Pauli, and Mario Fontana. 2012. “Numerical analysis and comparative study of the cross-sectional capacity of structural steel members in fire.” Journal of Structural Fire Engineering 3 (1): 19–36. Maia, ´ Elio, Carlos Couto, Paulo Vila Real, and Nuno Lopes. 2016. “Critical temperatures of class 4 cross-sections.” Journal of Constructional Steel Research 121: 370–382. Maraveas, Chrysanthos, Konstantinos Miamis, and Apostolos A Vrakas. 2012. “Fiberreinforced polymer-strengthened/reinforced concrete structures exposed to fire: a review.” Structural engineering international 22 (4): 500–513. Morgado, T, JR Correia, N Silvestre, and FA Branco. 2018. “Experimental study on the fire resistance of GFRP pultruded tubular beams.” Composites Part B: Engineering 139: 106– 116. Morgado, T, N Silvestre, and JR Correia. 2018a. “Simulation of fire resistance behaviour of pultruded GFRP beams–Part I: Models description and kinematic issues.” Composite Structures 187: 269–280. Morgado, T, N Silvestre, and JR Correia. 2018b. “Simulation of fire resistance behaviour of pultruded GFRP beams–Part II: Stress analysis and failure criteria.” Composite Structures 188: 519–530. Prachar, Martin, Michal Jandera, Frantisek Wald, and Bin Zhao. 2015. “Lateral TorsionalBuckling of Class 4 Steel Plate Beams at Elevated Temperature: Experimental and Numerical Comparison.” Journal of Structural Fire Engineering 6 (3): 223–236. 18 Rosa, IC, JP Firmo, JR Correia, and JAO Barros. 2019. “Bond behaviour of sand coated GFRP bars to concrete at elevated temperature–Definition of bond vs. slip relations.” Composites Part B: Engineering 160: 329–340. Rosa, IC, T Morgado, JR Correia, JP Firmo, and N Silvestre. 2018. “Shear Behavior of GFRP Composite Materials at Elevated Temperature.” Journal of Composites for Construction 22 (3): 04018010. Standard, International. 1999. “Fire-resistance tests elements of building construction. Part 1: General requirements.” . Wang, Ke, Ben Young, and Scott T Smith. 2011. “Mechanical properties of pultruded carbon fibre-reinforced polymer (CFRP) plates at elevated temperatures.” Engineering Structures 33 (7): 2154–2161. Wickstr¨om, Ulf. 1985. “Temperature analysis of heavily-insulated steel structures exposed to fire.” Fire Safety Journal 9 (3): 281–285. Wong, PMH, JM Davies, and YC Wang. 2004. “An experimental and numerical study of the behaviour of glass fibre reinforced plastics (GRP) short columns at elevated temperatures.” Composite structures 63 (1): 33–43. Yu, Bai, Vallee Till, and Keller Thomas. 2007. “Modeling of thermo-physical properties for FRP composites under elevated and high temperature.” Composites Science and Technology 67 (15-16): 3098–3109. 19