Evaluation of the reliability of optimized reinforced concrete beams

Correia, Rubens Silva; Bono, Giuliana Furtado Franca; Paliga, Charlei Marcelo

doi:10.1590/S1983-41952022000400009

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ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 15 (4) • 2022 • https://doi.org/10.1590/S1983-41952022000400009 copy

Evaluation of the reliability of optimized reinforced concrete beams

Avaliação da confiabilidade de vigas otimizadas de concreto armado

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

In the present research, the reliability of optimized reinforced concrete beams was evaluated in different design situations. Simply supported beams were optimized to find the dimensions and reinforcements of the cross-section that minimize costs, meeting the criteria of technical codes, through genetic algorithms. For each optimized beam, the reliability index was obtained in relation to the ultimate limit state of flexure with the iHLRF algorithm, considering the uncertainties of the resistance and load models, loads and resistances. It wa s verified that the reliability indexes, in general, were higher than the minimum value of 3.8, recommended by technical codes, in design situations with little live load. Through a parametric study, trends were identified for the reliability index according to the design parameters and characteristics of the beams.

Keywords:
beams; reinforced concrete; structural optimization; structural reliability

Concrete
Source	Type	Cost (R$/m³)
94965 - SINAPI PE 09/2019	C25	327.94
94966 - SINAPI PE 09/2019	C30	336.69
(interpolation between C30 and C40)	C35	353.99
CA-50 steel
Source	Diameter (mm)	Cost (R$/kg)
-	5	8.20
92760 - SINAPI PE 09/2019	6.3	8.20
92761 - SINAPI PE 09/2019	8	8.16
92762 - SINAPI PE 09/2019	10	6.67
92763 - SINAPI PE 09/2019	12.5	6.01
92764 - SINAPI PE 09/2019	16	5.68
92765 - SINAPI PE 09/2019	20	5.25
92766 - SINAPI PE 09/2019	25	5.82
Formwork
Source		Cost (R$/m²)
92448 - SINAPI PE 09/2019		78.07

Variables	Distribuition	Mean ( $μ$ )	Standard deviation ( $σ$ )
$θ_{R}$	Lognormal	1	0.05
$θ_{S}$	Lognormal	1	0.05
$g$	Normal	$1.05 g$	$0.10 μ$
$q$	Gumbel	$\frac{q}{(1 + 0.35 \times 0.25)}$	$0.25 μ$
$f_{c}$	Normal	$\frac{f_{c k}}{(1 - 1.645 \times 0.10)}$	$0.10 μ$
$f_{y}$	Normal	$\frac{f_{y k}}{(1 - 1.645 \times 0.05)}$	$0.05 μ$

Parameter	p-value
$L$	0
$(g + q)$	0
$r$	0
$f_{c k}$	0.3390
$L$ - $(g + q)$	0
$L$ - $r$	0.1411
$L$ - $f_{c k}$	0.9431
$(g + q)$ - $r$	0.0001
$(g + q)$ - $f_{c k}$	0.9837
$r$ - $f_{c k}$	0.7228

IBRACON - Instituto Brasileiro do Concreto Instituto Brasileiro do Concreto (IBRACON), Av. Queiroz Filho, nº 1700 sala 407/408 Torre D, Villa Lobos Office Park, CEP 05319-000, São Paulo, SP - Brasil, Tel. (55 11) 3735-0202, Fax: (55 11) 3733-2190 - São Paulo - SP - Brazil
E-mail: arlene@ibracon.org.br

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[1] Corresponding author: Rubens Silva Correia. E-mail: rubens.correia@ufpe.br