Comparison between exact and approximate methods for geometrically nonlinear analysis prescribed in design standards for steel and reinforced concrete structures

Lecchi, Laís De Bortoli; Ferreira, Walnório Graça; Costa, Paulo Manuel Mendes Pinheiro da Providência e; Sarmanho, Arlene Maria Cunha

doi:10.1590/S1983-41952022000100001

Acessibilidade / Reportar erro

Brasil

Revista IBRACON de Estruturas e Materiais

Español English

Brasil

Español English

sumário « anterior atual seguinte »

Sumário

ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 15 (1) • 2022 • https://doi.org/10.1590/S1983-41952022000100001 copy

Comparison between exact and approximate methods for geometrically nonlinear analysis prescribed in design standards for steel and reinforced concrete structures

Comparação entre métodos exato e aproximados de análise geometricamente não linear prescritos em normas de estruturas de aço e de concreto armado

Authorship SCIMAGO INSTITUTIONS RANKINGS

abstract:

Current practices in structural engineering demand ever-increasing knowledge and expertise concerning stability of structures from professionals in this field. This paper implements standardized procedures for geometrically nonlinear analysis of steel and reinforced concrete structures, with the objective of comparing methodologies with one another and with a geometrically exact finite element analysis performed with Ansys 14.0. The following methods are presented in this research: Load Amplification Method, from NBR 8800:2008; the $γ_{z}$ coefficient method, from NBR 6118:2014; the P-Delta iterative method and the $α_{c r}$ coefficient method, prescribed in EN 1993-1-1:2005. A bibliographic review focused on standardized approximate methods and models for consideration of material and geometric nonlinearities is presented. Numerical examples are included, from which information is gathered to ensure a valid comparison between methodologies. In summary, the presented methods show a good correlation of results when applied within their respective recommended applicability limits, of which, Eurocode 3 seems to present the major applicability range. The treated approximate methods show to be more suitable for regular framed structures subjected to regular load distributions.

Keywords:
global stability analysis; approximate nonlinear analysis; P-Delta iterative method; α_cr coefficient; ANSYS

}	Elastic analysis	$B_{1} - B_{2}$ Method	$γ_{Z}$ coefficient	P-Delta method	Eurocode method	Ansys
Amplification coefficients	-	$B_{1} = 1.00$	$γ_{Z} = 1.20$	$\frac{Δ_{2}}{Δ_{1}} = 1.13$	$β = 1.13$	$Δ_{2} / Δ_{1} = 1.21$
Amplification coefficients	-	$B_{2} = 1.20$	$γ_{Z} = 1.20$	$\frac{Δ_{2}}{Δ_{1}} = 1.13$	$β = 1.13$	$Δ_{2} / Δ_{1} = 1.21$
$Δ_{4}$ . node 4 [cm]	$15.22$	$18.96$	$22.11$	$17.18$	$20.40$	$24.3$
Bending moment Column 2 [kNm]	$96.8$	$63.9$	$75.7$	$75.4$	$75.6$	$64.2$
Axial force	$- 148.5$	$- 144.8$	$- 145.9$	$- 146.1$	$- 146.0$	$- 146.3$
Column 2 [kN]	$- 148.5$	$- 144.8$	$- 145.9$	$- 146.1$	$- 146.0$	$- 146.3$
Shear force	$36.1$	$36.1$	$38.0$	$33.3$	$36.3$	$31.4$
Column 2 [kN]	$36.1$	$36.1$	$38.0$	$33.3$	$36.3$	$31.4$

Bar number	Profile
1 - 4; 23 - 26	PS 500 x 300 x 16 x 8
12 - 15	PS 500 x 300 x 19 x 9,5
5 - 7; 16 - 18; 27 - 29	PS 500 x 300 x 12,5 x 8
8 - 11; 19 - 22; 30 - 33	PS 500 x 300 x 9,5 x 6,5
34 - 55	W 530 x 66

$n$	Coefficient $B_{2}$
$n$	1º floor	2º floor	3º floor	4º floor	5º floor	6º floor	7º floor	8º floor	9º floor	10º floor	11º floor
1	1.06	1.10	1.10	1.09	1.10	1.09	1.07	1.05	1.03	1.02	1.01
2	1.16	1.30	1.30	1.26	1.30	1.25	1.20	1.15	1.10	1.05	1.03
3	1.27	1.52	1.52	1.44	1.52	1.43	1.33	1.25	1.15	1.08	1.04
4	1.40	1.83	1.84	1.70	1.84	1.67	1.49	1.36	1.21	1.10	1.06
5	1.55	2.31	2.34	2.04	2.33	2.00	1.70	1.50	1.28	1.13	1.07

$n$	$B_{1}$ .	$γ_{Z}$	$α_{c r}$ .	$β$
1	1.0	1.08	12.68	1.09
2	1.0	1.18	6.19	1.19
3	1.0	1.29	4.23	1.31
4	1.0	1.43	3.17	1.46
5	1.0	1.61	2.54	1.65

$n$	$(Δ_{2} / Δ_{1})$ - P-Delta method.
$n$	1º floor	2º floor	3º floor	4º floor	5º floor	6º floor	7º floor	8º floor	9º floor	10º floor	11º floor
1	1.10	1.12	1.13	1.13	1.14	1.15	1.16	1.17	1.18	1.20	1.22
2	1.20	1.18	1.18	1.18	1.18	1.18	1.18	1.18	1.17	1.17	1.17
3	1.27	1.29	1.29	1.29	1.28	1.27	1.27	1.25	1.24	1.23	1.23
4	1.41	1.43	1.42	1.42	1.41	1.40	1.38	1.36	1.35	1.34	1.33
5	1.56	1.59	1.59	1.59	1.57	1.55	1.53	1.51	1.49	1.47	1.46

$n$	$(Δ_{2} / Δ_{1})$ - Ansys.
$n$	1º floor	2º floor	3º floor	4º floor	5º floor	6º floor	7º floor	8º floor	9º floor	10º floor	11º floor
1	1.07	1.08	1.08	1.08	1.08	1.08	1.08	1.07	1.07	1.07	1.07
2	1.15	1.17	1.18	1.18	1.18	1.17	1.17	1.16	1.15	1.15	1.14
3	1.27	1.28	1.29	1.29	1.29	1.28	1.27	1.26	1.25	1.24	1.23
4	1.39	1.42	1.43	1.43	1.43	1.42	1.40	1.38	1.36	1.35	1.39
5	1.54	1.58	1.60	1.60	1.60	1.59	1.56	1.53	1.51	1.49	1.48

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

Acompanhe os números deste periódico no seu leitor de RSS

[1] Corresponding author: Laís De Bortoli Lecchi. E-mail: laislecchi@gmail.com