COMPUTATIONAL INTELLIGENCE APPLIED IN OPTIMAL DESIGN OF WOODEN PLANE TRUSSES

Christoforo, André L.; Moraes, Matheus H. M. de; Fraga, Iuri F.; Pereira Junior, Wanderlei M.; Lahr, Francisco A. R.

doi:10.1590/1809-4430-Eng.Agric.v42nepe20210123/2022

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Sumário

Scientific Paper, Special Issue: Artificial Inteligence • Eng. agríc. (Online) 42 (spe) • 2022 • https://doi.org/10.1590/1809-4430-Eng.Agric.v42nepe20210123/2022 copy

COMPUTATIONAL INTELLIGENCE APPLIED IN OPTIMAL DESIGN OF WOODEN PLANE TRUSSES

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

The use of wood is widespread in rural constructions, and the truss systems stand out among its various applications. This specific system has several typologies and requires a thorough study to determine the most advantageous model for each project. The present study aims to apply the Computational Intelligence concepts to determine the minimum viable cross-section of a Howe truss. For the computational simulation, methods like Finite Elements were used to obtain the loads and the Firefly Algorithm for the optimization process, focusing on minimizing the total weight of the structural part. Studies were conducted varying the spans of the elements and the height to span ratio. The design assumptions for establishing the optimization method’s constraints follow the recommendations of the Brazilian standard for wood design, ABNT NBR 7190 (1997). Weights between 95.42 kg and 653.57 kg were obtained, and all optimization processes presented feasible solutions for the design constraints.

KEYWORDS
computational intelligence; optimization; timber truss; dicotyledonous

Parameter	Meaning	Adopted value
β ₀	Attractiveness among fireflies	0.90
N_gen	Number of generations	500
N_pop	Population size	20
α_min	Minimum randomness factor	0.20
α_max	Maximum randomness factor	1.00
R_p	Penalty factor	10⁵

Specification	Adopted
Class	Dicotyledonae C30
Typo of wood	Sawn
Loading class	Long duration
Humidity class	I
Equilibrium humidity	12%
Wood category	1st Category

f_c_0,d (MPa)	f_t_0,d (MPa)	E_c_0,ef (MPa)
10.29	13.36	6960

Truss	W_max (kg)	W_min (kg)	A (kg)	μ (kg)	$\bar{x}$ (kg)	σ (kg)	TF (%)
H-6-L/10	148.9771	106.7069	42.2703	116.3885	119.0252	9.1675	100
H-6-L/15	118.7732	97.8061	20.9671	106.3101	107.3664	5.6493	100
H-6-L/20	125.1609	95.4152	29.7457	113.7032	112.5430	6.8704	100
H-9-L/10	245.1870	168.5507	76.6363	206.8425	205.9876	17.2656	100
H-9-L/15	240.8623	175.9630	64.8993	208.7818	206.8520	17.8703	100
H-9-L/20	284.3665	238.2227	46.1438	261.7093	260.3088	12.0192	100
H-12-L/10	413.3496	322.7571	90.5925	361.5206	362.0176	29.7980	100
H-12-L/15	468.9180	265.1196	203.7984	389.5996	378.2887	57.1149	100
H-12-L/20	545.2604	304.9837	240.2767	425.1910	413.7167	45.3212	100
H-15-L/10	625.4143	510.1786	115.2357	555.2714	556.3199	30.6610	100
H-15-L/15	653.5657	387.0949	266.4707	511.3104	525.7424	54.3117	100
H-15-L/20	594.3057	411.7221	182.5837	550.7577	528.0167	53.5438	100

Truss	Design Variables
Truss	x₁ (cm²)	x₂ (cm²)	x₃ (cm²)	x₄ (cm²)
H-6-L/10	57.5	57.5	57.5	56.25
H-6-L/15	57.5	57.5	57.5	57.5
H-6-L/20	56.25	56.25	75	57.5
H-9-L/10	56.25	72.45	75	56.25
H-9-L/15	100.8	93.75	62.5	100.8
H-9-L/20	112.5	112.5	78.75	75
H-12-L/10	93.75	93.75	62.5	86.25
H-12-L/15	62.5	57.5	75	112.5
H-12-L/20	87.5	80	56.25	125
H-15-L/10	125	115	62.5	115
H-15-L/15	78.75	72.45	78.75	125
H-15-L/20	187.5	75	62.5	56.25

Truss	N	$\bar{x}$	σ	CI of 95%
H-6-L/10	50	- 0.7058	0.1720	(- 0.7785, - 0.6331)
H-6- L/15	50	- 0.6571	0.2135	(- 0.7372, - 0.5769)
H-6- L/20	50	- 0.6730	0.2299	(- 0.7506, - 0.5954)
H-9- L/10	50	- 0.5994	0.2165	(- 0.6721, - 0.5267)
H-9- L/15	50	- 0.6242	0.2235	(- 0.7043, - 0.5441)
H-9- L/20	50	- 0.6321	0.2395	(- 0.7097, - 0.5545)
H-12- L/10	50	- 0.5095	0.2836	(- 0.5822, - 0.4368)
H-12- L/15	50	- 0.4530	0.3457	(- 0.5331, - 0.3729)
H-12- L/20	50	- 0.5061	0.3498	(- 0.5838, - 0.4285)
H-15- L/10	50	- 0.4703	0.3389	(- 0.5430, - 0.3976)
H-15- L/15	50	- 0.4461	0.3393	(- 0.5263, - 0.3660)
H-15- L/20	50	- 0.5366	0.2778	(- 0.6142, - 0.4590)

Truss	N	$\bar{x}$	σ	CI of 95%
H-6-L/10	14	-0.7574	0.1875	(- 0.9171, - 0.5976)
H-6-L/15	14	-0.6253	0.3075	(- 0.7951, - 0.4556)
H-6-L/20	14	-0.5568	0.3476	(- 0.7346, - 0.3789)
H-9-L/10	14	-0.6356	0.3156	(- 0.7953, - 0.4758)
H-9-L/15	14	-0.6414	0.2961	(- 0.8112, - 0.4717)
H-9-L/20	14	-0.628	0.3042	(- 0.8058, - 0.4501)
H-12-L/10	14	-0.618	0.3294	(- 0.7778, - 0.4583)
H-12-L/15	14	-0.5442	0.2973	(- 0.7139, - 0.3744)
H-12-L/20	14	-0.4946	0.3477	(- 0.6724, - 0.3167)
H-15-L/10	14	-0.6509	0.3344	(- 0.8106, - 0.4911)
H-15-L/15	14	-0.4688	0.3607	(- 0.6386, - 0.2991)
H-15-L/20	14	-0.4957	0.3248	(- 0.6736, - 0.3179)

Associação Brasileira de Engenharia Agrícola SBEA - Associação Brasileira de Engenharia Agrícola, Departamento de Engenharia e Ciências Exatas FCAV/UNESP, Prof. Paulo Donato Castellane, km 5, 14884.900 | Jaboticabal - SP, Tel./Fax: +55 16 3209 7619 - Jaboticabal - SP - Brazil
E-mail: revistasbea@sbea.org.br

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[1] *Corresponding author. Federal University of Sao Carlos/ Sao Carlos - SP, Brazil. E-mail: matheus.h.h@hotmail.com