Reliability analysis of simply supported RC beam cross-sections in a fire situation according to Brazilian standards

Pires, Rodrigo Maffessoni; Gomes, Herbert Martins

doi:10.1590/S1983-41952024000400003

Rodrigo Maffessoni Pires

methodology

conceptualization

writing

data curation

Universidade Federal do Rio Grande do Sul - UFRGS, Programa de Pós-Graduação em Engenharia Civil, Porto Alegre, RS, Brasil

https://orcid.org/0009-0008-9857-5369

Herbert Martins Gomes

supervision

revision

data curation

Universidade Federal do Rio Grande do Sul - UFRGS, Programa de Pós-Graduação em Engenharia Civil, Porto Alegre, RS, Brasil

https://orcid.org/0000-0001-5635-1852

Corresponding author: Rodrigo Maffessoni Pires. E-mail: rodrigocivilfurg@gmail.com

Conflict of interest: Nothing to declare.

Editors: José Marcio Calixto, Guilherme Aris Parsekian.

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Figure 1
Difference of the stress-strain diagram of (a) concrete at ambient temperature and (b) concrete at high temperatures according to NBR 15200 [¹1 Associação Brasileira de Normas Técnicas, Projeto de Estruturas de Concreto em Situação de Incêndio, NBR 15200, 2012.].

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Figure 2
Determination of the reliability index by FORM.

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Figure 3
The reduced cross-section in different scenarios of fire.

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Figure 4
Determination of the ultimate resistant bending moment of a reinforced concrete beam according to Leite and Gomes [¹¹11 D. D. L. Leite and H. M. Gomes, “Reliability analysis of reinforced concrete sections for ultimate limit states,” in CILAMCE, Rio de Janeiro, Nov. 9-12 2021, pp. 1-7.].

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Figure 5
Standard fire from ISO 834.

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Figure 6
Scenarios of fire acting on a beam cross-section.

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Figure 7
Reference beam.

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Figure 8
Influence of the concrete cover on the reliability of the beams.

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Figure 9
Influence of the live-to-total load ratio on the reliability of the beams.

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Figure 10
Influence of the number of heated faces on the reliability of the beams

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Figure 11
Sensitivity analysis.

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Table 1
Reduction factors of the compressive strength of concrete (NBR 15200 [¹1 Associação Brasileira de Normas Técnicas, Projeto de Estruturas de Concreto em Situação de Incêndio, NBR 15200, 2012.]).

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Table 2
Ultimate strain of the concrete for different temperatures (NBR 15200 [¹1 Associação Brasileira de Normas Técnicas, Projeto de Estruturas de Concreto em Situação de Incêndio, NBR 15200, 2012.]).

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Table 3
Steel reduction factors

f_{y k}

and

E_{s}

(NBR 15200 [¹1 Associação Brasileira de Normas Técnicas, Projeto de Estruturas de Concreto em Situação de Incêndio, NBR 15200, 2012.]).

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Table 4
Random variables.

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Table 5
Nominal value of random variables for the reference beam

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

(25)

(26)

T (°C)	20	100	200	300	400	500	600	700	800	900	1000	1100	1200
$k_{c, θ}$	1.00	1.00	0.95	0.85	0.75	0.60	0.45	0.30	0.15	0.08	0.04	0.01	0.00

T (°C)	20	100	200	300	400	500	600	700	800	900	1000	1100
$ϵ_{c u θ} (‰)$	2.00	2.25	2.50	2.75	3.00	3.25	3.50	3.75	4.00	4.25	4.50	4.75

T (°C)	$k_{s, θ}$			$k_{E s, θ}$
	Tension		Compression CA-50 or CA-60	CA-50	CA-60
	CA-50	CA-60	Compression CA-50 or CA-60	CA-50	CA-60
20	1.00	1.00	1.00	1.00	1.00
100	1.00	1.00	1.00	1.00	1.00
200	1.00	1.00	0.89	0.90	0.87
300	1.00	1.00	0.78	0.80	0.72
400	1.00	0.94	0.67	0.70	0.56
500	0.78	0.67	0.56	0.60	0.40
600	0.47	0.40	0.33	0.31	0.24
700	0.23	0.12	0.10	0.13	0.08
800	0.11	0.11	0.08	0.09	0.06
900	0.06	0.08	0.06	0.07	0.05
1000	0.04	0.05	0.04	0.04	0.03
1100	0.02	0.03	0.02	0.02	0.02
1200	0.00	0.00	0.00	0.00	0.00

Random Variable	Distribution	Bias Factor	COV	Reference
Dead loads	Normal	1.00	0.10	Jovanović et al. [¹⁶16 B. Jovanović, R. Van Coile, D. Hopkin, N. E. Khorasani, D. Lange, and T. Gernay, “Review of current practice in probabilistic structural fire engineering: permanent and live load modelling,” Fire Technol., vol. 57, no. 1, pp. 1-30, Jan. 2021, http://dx.doi.org/10.1007/s10694-020-01005-w. http://dx.doi.org/10.1007/s10694-020-010... ]
Live loads	Gamma	0.20	0.95	Jovanović et al. [¹⁶16 B. Jovanović, R. Van Coile, D. Hopkin, N. E. Khorasani, D. Lange, and T. Gernay, “Review of current practice in probabilistic structural fire engineering: permanent and live load modelling,” Fire Technol., vol. 57, no. 1, pp. 1-30, Jan. 2021, http://dx.doi.org/10.1007/s10694-020-01005-w. http://dx.doi.org/10.1007/s10694-020-010... ]
Fire temperature	Normal	1.00	0.45	Eamon and Jensen [⁸8 C. D. Eamon and E. Jensen, “Reliability analysis of RC beams exposed to fire,” J. Struct. Eng., vol. 139, no. 2, pp. 212-220, Feb. 2013, http://dx.doi.org/10.1061/(ASCE)ST.1943-541X.0000614. http://dx.doi.org/10.1061/(ASCE)ST.1943-... ]
Steel yield strength	Normal	1.145	0.05	Eamon and Jensen [⁸8 C. D. Eamon and E. Jensen, “Reliability analysis of RC beams exposed to fire,” J. Struct. Eng., vol. 139, no. 2, pp. 212-220, Feb. 2013, http://dx.doi.org/10.1061/(ASCE)ST.1943-541X.0000614. http://dx.doi.org/10.1061/(ASCE)ST.1943-... ]
Steel modulus of elasticity	Lognormal	1.00	0.06	Hamutçuoglu and Scott [¹⁷17 O. M. Hamutçuoglu and M. H. Scott, “Finite element reliability analysis of bridge girders considering moment-shear interaction,” Struct. Saf., vol. 31, no. 5, pp. 356-362, Sep. 2009, http://dx.doi.org/10.1016/j.strusafe.2009.02.003. http://dx.doi.org/10.1016/j.strusafe.200... ]
Concrete cover	Beta [0;3c_nom]	1.06	0.26	Silva [¹⁸18 O. S. P. Silva, “Cobrimento de armaduras em estruturas de concreto armado: análise comparativa entre o valor especificado em projeto e o em execução em obras na cidade de Porto Alegre,” Undergraduate thesis, Dept. Eng. Civil, Univ. Fed. Rio Grande do Sul, Porto Alegre, Brazil, 2012.] and Van Coile et al. [¹⁹19 R. Van Coile, E. Annerel, R. Caspeele, and L. Taerwe, “Full-probabilistic analysis of concrete beams during fire,” J. Struct. Fire Eng., vol. 4, no. 3, pp. 165-174, Aug. 2013, http://dx.doi.org/10.1260/2040-2317.4.3.165. http://dx.doi.org/10.1260/2040-2317.4.3.... ]
Lower rebar position ( $d$ )	Normal	0.99	0.04	Eamon and Jensen [⁸8 C. D. Eamon and E. Jensen, “Reliability analysis of RC beams exposed to fire,” J. Struct. Eng., vol. 139, no. 2, pp. 212-220, Feb. 2013, http://dx.doi.org/10.1061/(ASCE)ST.1943-541X.0000614. http://dx.doi.org/10.1061/(ASCE)ST.1943-... ]
Concrete compressive strength	Normal	Equation 23	Equation 24	Santiago [²⁰20 W. C. Santiago, “Calibração baseada em confiabilidade dos coeficientes parciais de segurança das principais normas brasileiras de projeto estrutural,” Doctoral dissertation, Prog. Pós-Grad. Eng. Civil, Univ. São Paulo, São Carlos, Brazil, 2018.]
Beam width	Normal	1.01	0.04	Eamon and Jensen [⁸8 C. D. Eamon and E. Jensen, “Reliability analysis of RC beams exposed to fire,” J. Struct. Eng., vol. 139, no. 2, pp. 212-220, Feb. 2013, http://dx.doi.org/10.1061/(ASCE)ST.1943-541X.0000614. http://dx.doi.org/10.1061/(ASCE)ST.1943-... ]
Concrete thermal diff. coefficient	Normal	1.00	0.06	Eamon and Jensen [⁸8 C. D. Eamon and E. Jensen, “Reliability analysis of RC beams exposed to fire,” J. Struct. Eng., vol. 139, no. 2, pp. 212-220, Feb. 2013, http://dx.doi.org/10.1061/(ASCE)ST.1943-541X.0000614. http://dx.doi.org/10.1061/(ASCE)ST.1943-... ]
Model uncert. Resistant Bend. Mom.	Normal	1.02	0.06	Eamon and Jensen [⁸8 C. D. Eamon and E. Jensen, “Reliability analysis of RC beams exposed to fire,” J. Struct. Eng., vol. 139, no. 2, pp. 212-220, Feb. 2013, http://dx.doi.org/10.1061/(ASCE)ST.1943-541X.0000614. http://dx.doi.org/10.1061/(ASCE)ST.1943-... ]
Model uncert. Loading Bend. Mom.	Normal	1.00	0,05	Coelho [²¹21 T. A. P. Coelho, “Avaliação da confiabilidade de seções de vigas de concreto armado em situação de incêndio,” Master thesis, Prog. Pós-Grad. Eng. Estrut., Univ. Fed. Minas Gerais, Belo Horizonte, Brazil, 2018.]

Random Variable	Nominal Value
Dead load	12.5 kN/m
Live load	3 kN/m
Fire temperature^* * multiplicative random variables	1
Steel Yield strength	500 MPa
Steel Modulus of elasticity	210 GPa
Concrete cover	3 cm
Lower rebar position	36 cm
Concrete compressive strength of	25 MPa
Beam width	15 cm
Coefficient of thermal diffusivity of concrete	0.417×10^-6 m²/s
Model uncertainty of resistant bending moment ( $P$ )*	1
Model uncertainty of loading bending moment ( $Q$ )*	1

[1] Corresponding author: Rodrigo Maffessoni Pires. E-mail: rodrigocivilfurg@gmail.com

Brasil

Brasil

Reliability analysis of simply supported RC beam cross-sections in a fire situation according to Brazilian standards

Análise de confiabilidade de seções transversais de vigas simplesmente apoiadas de CA em situação de incêndio de acordo com normas brasileiras

Abstract