Dimensionamento otimizado de pilares mistos de aço preenchidos com concreto

Lourenção, Jéssica Salomão; Arpini, Paulo Augusto Tonini; Erlacher, Gabriel; Alves, Élcio Cassimiro

Jéssica Salomão Lourenção

Universidade Federal do Espírito Santo – UFES, Departamento de Engenharia Civil, Vitória, ES, Brasil

https://orcid.org/0000-0001-8920-9561

Paulo Augusto Tonini Arpini

Universidade Federal do Espírito Santo – UFES, Departamento de Engenharia Civil, Vitória, ES, Brasil

https://orcid.org/0000-0001-7066-5030

Gabriel Erlacher

Universidade Federal do Espírito Santo – UFES, Departamento de Engenharia Civil, Vitória, ES, Brasil

https://orcid.org/0000-0003-1063-0009

Élcio Cassimiro Alves

Universidade Federal do Espírito Santo – UFES, Departamento de Engenharia Civil, Vitória, ES, Brasil

https://orcid.org/0000-0001-6971-2645

Corresponding author: Élcio Cassimiro Alves. E-mail: elcio.calves1@gmail.com

Conflict of interest: Nothing to declare.

Author contributions: JSL: conceptualization, data curation, formal analysis, methodology, writing; PATA: data curation, formal analysis, methodology, writing; GE: formal analysis, writing; ECA: conceptualization, formal analysis, methodology, supervision, writing.

Editors: Túlio Nogueira Bittencourt, Guilherme Aris Parsekian.

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Figure 1
Groups of parameters that define the design variables.

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Figure 2
– Interaction diagrams for bending moment vs. axial force –(a) Design model I ABNT NBR 8800 [¹1 Associação Brasileira de Normas Técnicas, Projeto de Estruturas de Aço e de Estruturas Mistas de Aço e Concreto de Edifícios – Procedimento, ABNT NBR 8800, 2008.]; (b) Design model II ABNT NBR 8800 [¹1 Associação Brasileira de Normas Técnicas, Projeto de Estruturas de Aço e de Estruturas Mistas de Aço e Concreto de Edifícios – Procedimento, ABNT NBR 8800, 2008.]; (c) ABNT NBR 16239 [²2 Associação Brasileira de Normas Técnicas, Projeto de Estruturas de Aço e de Estruturas Mistas de Aço e Concreto de Edificações com Perfis Tubulares, ABNT NBR 16239, 2013.]; (d) EN 1994-1-1 [³3 European Commitee for Standardization, Design of Composite Steel and Concrete Structures. Part 1-1: General Rules and Rules for Buildings, EN 1994-1-1: Eurocode 4, 2004.].

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Figure 3
– Sequence of the four load cases analyzed and the respective axial forces and bending moments applied

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Figure 4
(a) Input screen of the developed software; (b) Output screen.

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Figure 5
– (a) Ratio R$/N_Sd; (b) Ratio AG/Original Solution; (c) Cost composition of composite filled columns (d) Composition of the resistance to normal forces of the composite filled column.

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Figure 6
– (a) Ratio R$/N_Sd; (b) Ratio AG/Original Solution; (c) Cost composition of composite filled columns (d) Composition of the resistance to normal forces of the composite filled column.

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Figure 7
– (a) Ratio R$/NSd; (b) Ratio AG/Original Solution; (c) Cost composition of composite filled columns (d) Composition of the resistance to normal forces of the composite filled column.

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Figure 5
– (a) Ratio R$/N_Sd; (b) Ratio AG/Original Solution; (c) Cost composition of composite filled columns (d) Composition of the resistance to normal forces of the composite filled column.

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Figure 6
– (a) Ratio R$/N_Sd; (b) Ratio AG/Original Solution; (c) Cost composition of composite filled columns (d) Composition of the resistance to normal forces of the composite filled column.

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Figure 7
– (a) Ratio R$/NSd; (b) Ratio AG/Original Solution; (c) Cost composition of composite filled columns (d) Composition of the resistance to normal forces of the composite filled column.

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Table 1
– Most notable studies on composite columns.

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Table 2
– Definition of design variables.

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Table 3
Cost of materials

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Table 4
– Optimization Results Example 1: L=3m; N_Sd=1000kN

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Table 5
– Optimization Results Example 2: L=4m; N_Sd=2000kN; M_x,Sd=132kN⸱m

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Table 6
– Optimization Results: L=3m; N_Sd=1500kN; M_x,Sd=132kN⸱m;M_y,Sd=76kN⸱m

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Author	Version of ABNT NBR 8800	ABNT NBR 16239	EN 1994-1-1	High strength concrete	Numerical Analysis	Theoretical-experimental analysis	Design	Continuous optimization	GA Optimization
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Caldas et al. [¹³13 R. B. Caldas, R. H. Fakury, and J. B. M. Sousa Jr., "Bases do dimensionamento de pilares mistos de aço e concreto segundo o projeto de revisão da ABNT NBR 8800," Rev. Esc. Minas, vol. 60, no. 2, pp. 271–276, 2007, http://dx.doi.org/10.1590/S0370-44672007000200009. http://dx.doi.org/10.1590/S0370-44672007... ]	1986				x		x
Oliveira [¹⁴14 W. L. A. Oliveira, “Análise teórico-experimental de pilares mistos preenchidos de seção circular,” M.S. thesis, EESC-USP, São Carlos, 2008.]						x
Dundu [¹⁰10 M. Dundu, "Compressive strength of circular concrete filled steel tube columns," Thin-walled Struct., vol. 56, pp. 62–70, 2012, http://dx.doi.org/10.1016/j.tws.2012.03.008. http://dx.doi.org/10.1016/j.tws.2012.03.... ]						x
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Papavasileiou et al. [¹⁵15 G. S. Papavasileiou, N. Nicolaou, and D. C. Charmpis, “Comparative assessment of buildings with pure steel or steel-concrete composite columns using structural design optimization,” in Proc. 4th Eccomas Thematic Conf. Comput. Methods Struct. Dyn. Earthq. Eng., Greece, 2013.]			x					x
Canales [²⁰20 A. F. Canales, “Estudo do dimensionamento de pilares de aço tubulares e pilares mistos de perfis tubulares preenchidos com concreto de acordo com a ABNT NBR 16239,” Undergraduate thesis, UTFPR, Campo Mourão, 2014.]	2008	x					x
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Lourenção and Alves [²²22 J. Lourenção and E. C. Alves, "Dimensionamento otimizado de pilares mistos preenchidos de aço e concreto," Rev. Port. Eng. Estrut., no. 8, pp. 33–48, Nov 2018.]	2008	x					x	x
PRESENT PAPER	2008	x	x	x			x		x

Variables	Rectangular Section	Square Section	Circular Section
Width	x_1,1 = b	x_1,1 = b = h	-
Height	x_1,2 = h	x_1,1 = b = h	-
Diameter	-	-	x₁ = d
Thickness	x_1,3 = t	x_1,2 = t	x_1,2 = t
Area of Steel	x_1,4 = A_a	x_1,3 = A_a	x_1,3 = A_a
Moment of inertia - x axis	x_1,5 = I_ax	x_1,4 = I_ax	x_1,4 = I_ax
Moment of inertia - y axis	x_1,6 = I_ay	x_1,5 = I_ay	x_1,5 = I_ay
Plastic section modulus - x axis	x_1,7 = Z_ax	x_1,6 = Z_ax	x_1,6 = Z_ax
Plastic section modulus - y axis	x_1,8 = Z_ay	x_1,7 = Z_ay	x_1,7 = Z_ay

Concrete f_ck(MPa)	Average Price (R$/m³)	Concrete f_ck(MPa)	Average Price (R$/m³)	Source
20	295,00	55	520,13	Table SINAPI – Price of materials (Caixa Econômica Federal). Reference month: February/2020. Locality: Vitória/ES
25	307,42	60	584,82
30	317,77	65	640,46
35	329,15	70	696,09
40	341,57	75	751,73
45	384,01	80	807,36
50	455,43	85	891,53
		90	952,81
Steel CA50	5,01
VMB350	4,50			Vallourec. Reference: March/2020
VMB350	5,50			Vallourec. Reference: March/2020

ABNT NBR 8800		D mm	t mm	f_ck MPa	N_Rd kN	M_x,Rd kN⸱m	M_y,Rd kN⸱m	N	ϕ mm	δ	CT	RA
		D mm	t mm	f_ck MPa	N_Rd kN	M_x,Rd kN⸱m	M_y,Rd kN⸱m				R$
		150:150	12,5	30	1555	82,29	82,29				904,60
Lourenção e Alves[22] Interior Point Method	ABNT NBR 16239	140,1:141,1	3,6	90	1000,0	27,3	27,3				306,50	N_Rd
	ABNT NBR 8800	168,3	5	75	1163,6	37,1	37,1			0,37	316,74	N_Rd
Circular without Reinforcement	ABNT NBR 161239	273	6,4	90	1016,8	35,2	35,2			0,52	292,52	N_Rd
	EN 1994- 1-1	323,8	6,4	40	1034,2	39,5	39,5			0,46	306,89	N_Rd
Circular with Reinforcement	ABNT NBR 8800	323,8	6,4	65	1537,2	90,9	90,9	6	12,5	0,56	570,03	N_Rd
	ABNT NBR 16239	273	6,4	55	1692,5	90,9	90,9	6	12,5	0,56	570,03	N_Rd
	EN 1994-1-1	323,8	6,4	35	1080,7	47,3	47,3	7	10	0,54	487,09	N_Rd
Square without Reinforcement	ABNT NBR 8800	140	6,4	90	1188,9	43,2	43,2			0,46	468,4	N_Rd
	ABNT NBR 161239	130	5	80	1002,2	30,3	30,3			0,44	341,8	N_Rd
	EN 1994-1-1	140	5	85	1001,7	38,8	38,8			0,45	378,02	N_Rd
Square without Reinforcement	ABNT NBR 8800	130	6,4	65	1014,7	37,3	37,3	4	12,5	0,48	474,11	N_Rd
	ABNT NBR 16239	120	5,6	90	1001,0	28,8	28,8	6	10	0,41	409,29	N_Rd
	EN 1994-1-1	140	5	70	1001,8	41,6	41,6	12	10	0,37	479,32	N_Rd
Rectangular without Reinforcement	ABNT NBR 8800	130:180	6,4	70	1217,1	59,6	45,7			0,5	512,32	N_Rd
	ABNT NBR 161239	120:160	5	70	1011,6	39,2	30,8			0,45	367,29	N_Rd
	EN 1994-1-1	120:170	6,4	70	1037,6	56,4	42,6			0,55	481,98	N_Rd
Rectangular with Reinforcement	ABNT NBR 8800	150:200	6,4	25	1293,8	74,5	60,0	6	10	0,62	633,62	N_Rd
	ABNT NBR 16239	150:200	6,4	25	1463,4	74,5	60,0	6	10	0,62	633,62	N_Rd
	EN 1994-1-1	150:200	6,4	25	1191,3	83,8	67,0	4	10	0,78	615,09	N_Rd

Canales [²⁰20 A. F. Canales, “Estudo do dimensionamento de pilares de aço tubulares e pilares mistos de perfis tubulares preenchidos com concreto de acordo com a ABNT NBR 16239,” Undergraduate thesis, UTFPR, Campo Mourão, 2014.] ABNT NBR 16239		D mm	t mm	f_ck MPa	N_Rd kN	M_x,Rd kN⸱m	M_y,Rd kN⸱m	n	ϕ mm	δ	CT	RA
		D mm	t mm	f_ck MPa	N_Rd kN	M_x,Rd kN⸱m	M_y,Rd kN⸱m				R$
		323,8	10,3	30	3430	260,06	260,06				1525,17
Lourenção e Alves [22] (Interior Point Method)	ABNT NBR 16239	286,2	5,7	90	4377,0	252,8	252,8			0,28	935,80
Circular without Reinforcement	ABNT NBR 8800	323,8	7,1	80	4803,01	206,317	206,317			0,28	1240,70	IA-I
	ABNT NBR 161239	273	6,4	90	4001,76	132,34	132,34			0,27	960,00	IA-III
	EN 1994-1-1	323,8	6,4	40	3209,85	193,185	193,185			0,44	1005,30	IA-IV
Circular with Reinforcement	ABNT NBR 8800	323,8	6,4	65	4359,09	219,892	219,892	6	12,5	0,28	1211,90	IA-I
	ABNT NBR 16239	273	6,4	55	3275,01	153,045	153,045	6	12,5	0,35	983,80	IA-III
	EN 1994-1-1	323,8	6,4	35	3206,29	213,112	213,112	6	10	0,45	1075,60	IA-IV
Square without Reinforcement	ABNT NBR 8800	270	8	80	4317,56	224,6	224,6			0,38	1648,49	IA-I
	ABNT NBR 161239	240	6,4	70	3310,65	138,6	138,6			0,38	1157,38	IA-III
	EN 1994-1-1	250	6,4	80	3309,53	166,2	166,2			0,37	1221,24	IA-IV
Square without Reinforcement	ABNT NBR 8800	260	8	90	4425,6	214,7	210,9	6	12,5	0,34	1713,77	IA-I
	ABNT NBR 16239	240	6,4	65	3425,52	145,8	149,2	6	12,5	0,36	1261,73	IA-III
	EN 1994-1-1	250	6,4	75	3380,92	171,2	173,6	6	10	0,36	1282,86	IA-IV
Rectangular without Reinforcement	ABNT NBR 8800	200:350	8	75	3643,17	271,241	168,741			0,4	1624,95	IA-I
	ABNT NBR 161239	200:300	6,4	60	2978,92	173,011	123,176			0,41	1139,44	IA-III
	EN 1994-1-1	200:300	6,4	60	2658,45	189,441	135,15			0,42	1139,40	IA-IV
Rectangular with Reinforcement	ABNT NBR 8800	240:280	7,1	85	4239,9	225,889	183,62	8	16	0,3	1686,18	IA-I
	ABNT NBR 16239	200:300	6,4	55	3082,79	182,604	130,653	6	12,5	0,39	1241,36	IA-III
	EN 1994-1-1	200:320	6,4	70	2643,99	254,391	170,676	4	12,5	0,48	1339,07	IA-IV

Original Solution- Rectangular ABNT NBR 8800:2008		D mm	t mm	f_ck MPa	N_Rd kN	M_x,Rd kN⸱m	M_y,Rd kN⸱m	n	ϕ mm	D	CT	RA
		D mm	t mm	f_ck MPa	N_Rd kN	M_x,Rd kN⸱m	M_y,Rd kN⸱m				R$
		180:300	12,5	40	3890	405,78	227,01				1.494,20
Lourenção e Alves [22] (Interior Point Method	ABNT NBR 8800	200:400	7,9	90	5098,0	341,6	186,5				1404,60	IA-I
Circular without Reinforcement	ABNT NBR 8800	355,6	8	55	5034,71	270,0	270,0			0,37	1067,60	IA-I
	ABNT NBR 161239	323,8	8	30	3303,19	209,6	209,6			0,54	912,40	IA-III
	EN 1994-1-1	323,8	6,4	45	3614,66	195,2	195,2			0,41	763,60	IA-IV
Circular with Reinforcement	ABNT NBR 8800	323,8	7,1	80	5563,45	257,8	257,8	9	12,5	0,26	1060,80	IA-I
	ABNT NBR 16239	323,8	6,4	35	3534,47	209,9	209,9	6	12,5	0,41	838,00	IA-III
	EN 1994-1-1	323,8	6,4	40	3587,69	215,3	215,3	6	10	0,42	809,60	IA-IV
Square without Reinforcement	ABNT NBR 8800	290	8	90	5597,35	255,6	255,6			0,33	1346,50	IA-I
	ABNT NBR 161239	270	8	40	3441,23	214,6	214,6			0,55	1146,30	IA-III
	EN 1994-1-1	260	6,4	75	3873,78	180,4	180,4			0,37	964,10	IA-IV
Square without Reinforcement	ABNT NBR 8800	290	8	65	4896,18	267,0	267,0	4	16	0,38	1371,10	IA-I
	ABNT NBR 16239	260	8	55	4069,92	209,0	209,0	4	16	0,44	1216,10	IA-III
	EN 1994-1-1	260	6,4	70	3943,11	185,7	185,7	6	10	0,48	1009,50	IA-IV
Rectangular without Reinforcement	ABNT NBR 8800	250:320	8,8	80	5067,5	290,9	235,8				1413,50	IA-I
	ABNT NBR 161239	200:250	8	40	3479,57	230,7	199,9			0,54	1148,30	IA-III
	EN 1994-1-1	240:280	6,4	75	3801,71	192,0	168,4			0,38	963,20	IA-IV
Rectangular with Reinforcement	ABNT NBR 8800	250:320	8	80	5154,12	286,7	226,1	6	12,5	0,35	1391,10	IA-I
	ABNT NBR 16239	240:280	8	45	3706	219,1	193,1	4	16	0,48	1191,40	IA-III
	EN 1994-1-1	240:280	6,4	80	3085,56	236,9	210,3	6	10	0,48	1028,90	IA-IV

E_{c} = \propto_{i} E_{c i} \{\begin{matrix} \propto_{i} = 0,8 + 0,2 \frac{f_{c k}}{80} \leq 1.0 \\ E_{c i} = \{\begin{matrix} \propto_{e} 5600 \sqrt{f_{c k}} 20 M P a \leq f_{c k} \leq 50 M P a \\ \propto_{e} 21500 \sqrt[3]{f_{c k} + 1,25} 50 M P a < f_{c k} \leq 90 M P a \end{matrix} \end{matrix}

η_{c} = \{\begin{matrix} η_{c 0} (1 + 10 \frac{e}{D}) f o r \frac{e}{D} \leq 0,1 \\ 0 f o r \frac{e}{D} > 0,1 \\ η_{c 0} = 4,9 - 18,5 λ + 17 λ^{2} \end{matrix}

η_{a} = \{\begin{matrix} η_{a 0} + (1 - η_{a 0}) (10 \frac{e}{D})) f o r \frac{e}{D} \leq 0,1 \\ 1 f o r \frac{e}{D} > 0,1 \\ η_{a 0} = 0,25 (3 + 2 λ) \end{matrix}

[1] Corresponding author: Élcio Cassimiro Alves. E-mail: elcio.calves1@gmail.com

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Dimensionamento otimizado de pilares mistos de aço preenchidos com concreto

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