Probability of failure of RC columns in fire situation

Preuss, Arthur de Caneda; Gomes, Herbert Martins

doi:10.1590/S1983-41952024000100002

Arthur de Caneda Preuss

methodology

conceptualization

writing

data curation

Universidade Federal do Rio Grande do Sul - UFRGS, Graduate Program in Civil Engineering, Porto Alegre, RS, Brasil

https://orcid.org/0000-0001-6210-4196

Herbert Martins Gomes

supervision

revision

data curation

Universidade Federal do Rio Grande do Sul - UFRGS, Graduate Program in Civil Engineering, Porto Alegre, RS, Brasil

Universidade Federal do Rio Grande do Sul - UFRGS, Graduate Program in Mechanical Engineering, Porto Alegre, RS, Brasil

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

Corresponding author: Arthur de Caneda Preuss. E-mail: arthurcaneda@hotmail.com

Conflict of interest: Nothing to declare.

Author contributions: ACP: methodology, conceptualization, writing, data curation; HMG: supervision, revision, data curation.

Editors: Diogo Ribeiro, Guilherme Aris Parsekian.

Column	(1) Experimental ultimate load [ $k N$ ]	(2) Ultimate load, this paper [ $k N$ ]	(3) Padre [²⁹29 E. P. G. Padre, "Desenvolvimento de um algoritmo computacional para verificação de seções de concreto armado submetidas à flexão composta oblíqua em situação de incêndio," M.S. Dissertation, Univ. Fed. Viçosa, Viçosa, 2017.] [ $k N$ ]	(1)/(2)	(1)/(3)
1	2325.00	2428.36	2241.54	0.957	1.037
2	2060.00	1883.00	2074.42	1.094	0.993
3	1902.00	1982.17	1998.28	0.960	0.952
4	1480.00	1364.04	1370.48	1.085	1.080

Random variable	Probability Density Function	Mean value ( $μ$ )	Coefficient of variation ( $V$ )	Standard deviation ( $σ$ )
Compressive strength ( $f_{c}$ ) $[M P a]$	Gaussian	$1.17 {∙ f}_{c k}$ a	$σ_{f c} / f_{c m}$ b	$0.15 e^{[- 0.036 (f_{c k} - 20)] μ_{f_{c}}}$ a,c
Steel yielding strength ( $f_{y}$ ) $[M P a]$	Log-normal d	$1.09 ∙ f_{y k}$	$0.05$	$μ_{f y} ∙ 0.05$
Cross-section dimensions ( $d'$ , $b$ , $h$ ) e $[c m]$	Gaussian	Design nominal values	$\frac{σ}{μ}$	$0.50$ f
Live load ( $G$ ) $[k N]$	Gaussian	$1.05 {∙ G}_{k, 50}$ g	$0.10$	$μ_{G} ∙ 0.10$
Dead load ( $Q$ ) $[k N]$	Gumbel	$0.24 {∙ Q}_{k, 50}$ h	$0.65$	$μ_{Q} ∙ 0.65$
Resistance modeling error ( $θ_{R}$ ) $[d i m e n s i o n l e s s]$	Log-normal i	$1.00$	$0.05$	$0.05$
Load modeling error ( $θ_{S}$ ) $[d i m e n s i o n l e s s]$	Log-normal i	$1.00$	$0.05$	$0.05$
Temperature ( $T$ ) $[° C]$	Gaussian	Obtained by ISO 834 [²⁷27 International Organization for Standardization, Fire Resistance Test Elements of Building Construction, ISO 834:2014, 2014.]	$0.45$ j	$μ_{T} ∙ 0.45$

a) Expression extracted from Leite and Gomes [³¹31 D. L. Leite and H. M. Gomes, "Reliability analysis of reinforced concrete sections for ultimate limit states," in Proceedings of the Joint XLII Ibero-Latin-American Congress on Computational Methods in Engineering, Rio de Janeiro, 2021, pp. 1-7.]; b) A variable coefficient of variation of the compressive strength for concrete is considered such that it decreases as the compressive strength increases, representing the variability of the resistances associated with production control; c) fck should be in MPa for σfc evaluation; d) As presented by Machado [³²32 E. R. Machado, "Avaliação da confiabilidade de estruturas de concreto armado," M.S. Dissertation, Univ. Fed. Minas Gerais, Belo Horizonte, 2001.], the Log-normal distribution is more adequate for this random variable; e) d' is the distance from the reinforcement CG to the concrete face; f) Presented value by Damas [³³33 A. P. Damas, "Estudo de confiabilidade no projeto de pilares esbeltos de concreto de alta resistência," M.S. Dissertation, Univ. Fed. Rio Gde. Sul, Porto Alegre, 2015.]; g) Expression presented in Galambos et al. [³⁴34 T. V. Galambos, B. Ellingwood, J. G. MacGregor, and C. A. Cornell, "Probability-based load criteria: assessment of current design practice," J. Struct. Eng., vol. 108, no. 5, pp. 959-977, May 1982, http://dx.doi.org/10.1061/JSDEAG.0005958.
http://dx.doi.org/10.1061/JSDEAG.0005958... ]; h) This consideration is made in Coelho [¹¹11 T. A. P. Coelho, "Avaliação da confiabilidade de seções de vigas de concreto armado em situação de incêndio," M.S. Dissertation, Univ. Fed. Minas Gerais, Belo Horizonte, 2018.], whose objective is to transform the maximum loading statistic corresponding to a service life of 50 years into an arbitrary instant, consistent with a load in a fire situation; i) As presented in Ellingwood and Galambos [³⁵35 B. Ellingwood and T. V. Galambos, "Probability-based criteria for structural design," Struct. Saf., vol. 1, no. 1, pp. 15-26, 1982, http://dx.doi.org/10.1016/0167-4730(82)90012-1.
http://dx.doi.org/10.1016/0167-4730(82)9... ]; j) Value shown in Eamon and Jensen [⁶6 C. D. Eamon and E. Jensen, "Reliability analysis of prestressed concrete beams exposed to fire," Eng. Struct., vol. 43, pp. 69-77, Oct. 2012, http://dx.doi.org/10.1016/j.engstruct.2012.05.016.
http://dx.doi.org/10.1016/j.engstruct.20... ]-[⁸8 C. D. Eamon and E. Jensen, "Reliability analysis of reinforced concrete columns exposed to fire," Fire Saf. J., vol. 62, no. part C, pp. 221-229, Nov. 2013, http://dx.doi.org/10.1016/j.firesaf.2013.10.002.
http://dx.doi.org/10.1016/j.firesaf.2013... ].

x_{2 D} = \sqrt{\frac{\frac{a}{a_{c}} t}{e x p [4.5 + \frac{n_{w} - \sqrt{n_{w}^{2} - (2 n_{w} - 1) \frac{480}{∆ θ_{f}}}}{0.18 {(2 n}_{w} - 1)}]}}

σ_{s, θ} = \{\begin{matrix} ε_{s, θ} ∙ E_{s, θ}; i f 0 \leq ε_{s, θ} \leq ε_{p, θ} \\ f_{p, θ} - c + \frac{b}{a} ∙ \sqrt{a^{2} - {(ε_{y, θ} - ε_{s, θ})}^{2}}; i f ε_{p, θ} \leq ε_{s, θ} \leq ε_{y, θ} \\ f_{y, θ}; i f ε_{y, θ} \leq ε_{s, θ} \leq ε_{t, θ} \\ f_{y, θ} ∙ [1 - (\frac{ε_{s, θ} - ε_{t, θ}}{ε_{u, θ} - ε_{t, θ}})]; i f ε_{t, θ} \leq ε_{s, θ} \leq ε_{u, θ} \\ 0; i f ε_{s, θ} \geq ε_{u, θ} \end{matrix}

c = \frac{{(f_{y, θ} - f_{p, θ})}^{2}}{(ε_{y, θ} - ε_{p, θ}) ∙ E_{s, θ} - 2 ∙ (f_{y, θ} - f_{p, θ})}

[1] Corresponding author: Arthur de Caneda Preuss. E-mail: arthurcaneda@hotmail.com

Brasil

Brasil

Probability of failure of RC columns in fire situation

Probabilidade de falha de pilares de concreto armado em situação de incêndio

Abstract