Abstract
To obtain an accurate estimation of the residual bearing capacities of concrete T-shaped beams after fire exposure, a calculation method combined the finite element (FE) thermal simulation and analytical equilibrium equation was established on a basis of an experimental study of fire (high-temperature) exposure. The effect of the concrete crack size under fire exposure on the post-fire residual bearing capacity was carefully considered in the calculation method. The influences of the load ratio, reinforcement ratio, height-to-width ratio and concrete cover thickness on the residual bearing capacity of a concrete beam after fire exposure were studied, and then a calculation formula for predicting the residual bearing capacity of a concrete T-shaped beam considering fire cracks was proposed according to these influencing factors. The results show that the height-to-width ratio and the reinforcement ratio have a great influence on the residual bearing capacity of the T-shaped beam after fire exposure; these ratios are positively correlated with the residual bearing capacity. The load ratio of the T-shaped beam also has a great influence on the residual bearing capacity of the beam after fire exposure; this ratio is negatively correlated with the residual bearing capacity. The thickness of the concrete cover has little effect on the residual bearing capacity. Compared with that of the finite element simulation results, the calculation accuracy of the residual bearing capacity formula after fire exposure is satisfactory; thus, this work can provide a reference for the calculation of the residual bearing capacity of concrete T-shaped beams after fire exposure.
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References
Xu QF, Han CQ, Wang YC (2015) Experimental and numerical investigations of fire resistance of continuous high strength steel reinforced concrete T-beams. Fire Saf J 78:142–154. https://doi.org/10.1016/j.firesaf.2015.09.001
Ba GZ, Miao JJ, Zhang WP (2016) Influence of cracking on heat propagation in reinforced concrete structures. J Struct Eng 142(7):04016035. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001483
Wu B, Xiong W, Wen B (2014) Thermal fields of cracked concrete members in fire. Fire Saf J 66:15–24. https://doi.org/10.1016/j.firesaf.2014.04.003
Ervine A, Gillie M, Stratford TJ (2012) Thermal propagation through tensile cracks in reinforced concrete. J Mater Civ Eng 24(5):516–522. https://doi.org/10.1061/(ASCE)MT.1943-5533.0000417
Li Z, Xiao J, Xie Q (2020) Reliability analysis of the residual moment capacity of high-strength concrete beams after elevated temperatures. Struct Concr. https://doi.org/10.1002/suco.202000444
El-Hawary MM, Ragab AM, El-Azim AA (1996) Effect of fire on flexural behaviour of R.C. beams. Constr Build Mater 10(2):147–150
Kodur VKR, Dwaikat MB, Fike RS (2010) An approach for evaluating the residual strength of fire-exposed RC beams. Mag Concr Res 62(7):479–488. https://doi.org/10.1680/macr.2010.62.7.479
Cai B, Li B, Fu F (2020) Finite element analysis and calculation method of residual flexural capacity of post-fire RC beams. Inter J Concr Struct Mater. https://doi.org/10.1186/s40069-020-00428-7
Zheng WZ, Hou XM (2008) Experiment and analysis on the mechanical behaviour of PC simply-supported slabs subjected to fire. Adv Struct Eng 11(1):71–89. https://doi.org/10.1260/136943308784069513
Yuan F, Wu YF (2019) Application of RC flexural theorems for member design under elevated temperature. Eng Struct. https://doi.org/10.1016/j.engstruct.2019.109762
Kodur VKR, Agrawal A (2016) An approach for evaluating residual capacity of reinforced concrete beams exposed to fire. Eng Struct 110:293–306. https://doi.org/10.1016/j.engstruct.2015.11.047
Venkatesh KK, Ankit A (2016) Critical factors governing the residual response of reinforced concrete beams exposed to fire. Fire Technol 52(4):967–993. https://doi.org/10.1007/s10694-015-0527-5
ABAQUS (2014) Version 6.14.4 documentation. Providence (RI): Dassault Systemes Simulia Corp.
ISO 834–1 (1999) Fire resistance tests-elements of building construction. Part 1: General requirement. Geneva, Switzerland.
Lie TT, Celikkol B (1991) Method to calculate the fire resistance of circular reinforced concrete columns. ACI Mater J 81(1):84–91
EN 1992–1–2 (2004) Eurocode 2 design of concrete structures, part 1–2: general rules-structural fire design. European Committee for Standardization.
Dwaikat MB, Kodur VKR (2009) Hydrothermal model for predicting fire-induced spalling in concrete structural systems. Fire Saf J 44:425–434. https://doi.org/10.1016/j.firesaf.2008.09.001
Gao WY, Dai JG, Teng JG et al (2013) Finite element modeling of reinforced concrete beams exposed to fire. Eng Struct 52:488–501. https://doi.org/10.1016/j.engstruct.2013.03.017
Zhu Y (2009) Study on fire resistance of concrete beams with CFRP bars considering crack effect. Master’s Degree Thesis, Harbin Institute of Technology [in Chinese]
Lu LM, Yong YC, Robby TL (2015) Influencing factors for fire performance of simply supported RC beams with implicit and explicit transient creep strain material models. Fire Saf 73:29–36. https://doi.org/10.1016/j.firesaf.2015.02.009
Hawileh RA, Naser M, Zaidan W, Rasheed HA (2009) Modeling of insulated CFRP-strengthened reinforced concrete T-beam exposed to fire. Eng Struct 31(12):3072–3079. https://doi.org/10.1016/j.engstruct.2009.08.008
Zhang HY, Li QY, Kodur V, Lv HR (2021) Effect of cracking and residual deformation on behavior of concrete beams with different scales under fire exposure. Eng Struct. https://doi.org/10.1016/j.engstruct.2021.112886
Gernay T, Franssen J-M (2012) A formulation of the Eurocode 2 concrete model at elevated temperature that includes an explicit term for transient creep. Fire Saf J 51:1–9. https://doi.org/10.1016/j.firesaf.2012.02.001
EN 1994–1–2 (2005) Eurocode 4 design of composite steel and concrete structures. Part 1–2: general rules-structural fire design. European Committee for Standardization.
IBM SPSS Statistics version 22 (IBM SPSS Inc., Chicago, USA)
Molkens T, Van Coile R, Gernay T (2017) Assessment of damage and residual load bearing capacity of a concrete slab after fire: applied reliability-based methodology. Eng Struct 150:969–985
Funding
This research was supported by the National Natural Science Foundation of China (Grant No. 52178487, 52008384); Natural Science Foundation of Shandong Province (ZR2021ME228, ZR2020QE255); Postdoctoral Research Foundation of China (Grant No.2018M632640); Shandong Provincial Postdoctoral Science Foundation (2019057); Qingdao Postdoctoral Science Foundation (Grant No. 2018103) and First-Class Discipline Project Funded by the Education Department of Shandong Province. The financial support is highly appreciated.
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Liu, C.W., Mao, J.Y., Dong, K. et al. Calculation Method of the Residual Bearing Capacities of Concrete T-Shaped Beams Considering the Effect of Fire Cracks. Fire Technol 59, 305–329 (2023). https://doi.org/10.1007/s10694-022-01324-0
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DOI: https://doi.org/10.1007/s10694-022-01324-0