Floors number influence on the instability parameter of reinforced concrete frame-braced buildings

ELLWANGER, R. J.

doi:10.1590/S1983-41952019000500005

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Articles • Rev. IBRACON Estrut. Mater. 12 (05) • Sep-Oct 2019 • https://doi.org/10.1590/S1983-41952019000500005 copy

Floors number influence on the instability parameter of reinforced concrete frame-braced buildings

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

This work aims to investigate the floors number influence on the instability parameter limit α₁ of reinforced concrete frame-braced buildings; it succeeds another work in this field of knowledge, in which the same question was investigated for wall- and core-braced buildings. Initially, it is showed how the ABNT NBR 6118:2014 (Brazilian code for concrete structures design) defines when a second order analysis is needed. Topics concerning to physical nonlinearity consideration and to the lateral deflection components of frames are also presented. It follows an analytical study that led to the derivation of a method for determining the limit α₁ as a function of the floors number and the relation between bending and shear stiffness. Finally, some examples are presented and their results are used for checking the method accuracy.

Keywords:
instability; bracing structures; second order analysis.

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

[TFN1] ¹
Values found in the examples;

[TFN2] ²
values predicted from table 2;

[TFN3] ³
α₁ (2) with (EI)_sec / E_CSI_C factor improvement;

[TFN4] ⁴
Differences between α¹ and α₁ ³.

Number of floors	α₁
1	0.42
2	0.47
3	0.49
≥ 200	0.65

Number of floors	Values of $\bar{K}$
Number of floors	500	300	250	200	150	100	80	60	40	20
4	0.493	0.494	0.494	0.494	0.495	0.496	0.497	0.498	0.500	0.506
5	0.498	0.499	0.499	0.499	0.500	0.502	0.503	0.505	0.509	0.518
6	0.501	0.502	0.503	0.503	0.505	0.507	0.509	0.512	0.516	0.528
8	0.505	0.507	0.508	0.510	0.512	0.516	0.519	0.523	0.531	0.548
10	0.509	0.512	0.513	0.516	0.519	0.525	0.529	0.535	0.545	0.564
12	0.512	0.516	0.518	0.521	0.526	0.534	0.539	0.546	0.557	0.578
16	0.519	0.526	0.529	0.533	0.540	0.551	0.557	0.566	0.579	0.598
20	0.526	0.535	0.540	0.545	0.553	0.566	0.573	0.582	0.595	0.611
25	0.535	0.548	0.553	0.560	0.569	0.582	0.590	0.598	0.609	0.622
30	0.544	0.559	0.565	0.573	0.582	0.596	0.602	0.610	0.619	0.629
40	0.563	0.580	0.586	0.594	0.603	0.614	0.619	0.624	0.631	0.638
50	0.579	0.596	0.602	0.609	0.616	0.625	0.629	0.633	0.637	0.642
100	0.623	0.633	0.636	0.639	0.642	0.645	0.646	0.647	0.649	0.650
150	0.639	0.644	0.645	0.647	0.648	0.650	0.650	0.651	0.652	0.652

Example	1	2	3	4	5	6	7	8	9	10
N. of floors	5	5	10	10	20	20	30	30	50	50
Height (m)	15	15	30	30	60	60	90	90	150	150
N. of frames	3	3	5	3	5	5	9	7	13	11
Spacing (m)	10	7.5	7.5	7.5	7.5	4	3.75	5	2.5	3
N. of bays	1	3	1	3	1	3	1	3	1	3
Dimension l₁ (m)	12	16	12	16	12	18	12	23	20	23
Dimension l₂ (m)	−	10	−	10	−	12	−	17	−	17

Example	Beams	Columns
1	25 x 68	25 x 47
2	19 x 47	19 x 47
3	25 x 68	25 x 68
4	20 x 60	20 x 60
5	40 x 76	40 x 100
6	23 x 60	30 x 89
7	33 x 78	40 x 130
8	29 x 65	29 x 117
9	64 x 193	64 x 130
10	+ edges 45 x 12	32 x 82
	32 x 125
	+ edges 30 x 12

Example	I_C (m⁴)	$\bar{K}$	(EI)_sec / E_CSI_C
1	0.422	169	0.687
2	0.517	456	0.670
3	3.268	173	0.650
4	3.952	280	0.673
5	22.17	175	0.700
6	35.15	449	0.641
7	66.81	244	0.727
8	133.4	375	0.696
9	299.7	19.5	0.986
10	342.5	69.5	0.967

Example	α ¹	α₁ ²	α₁ ³	Difference ⁴
1	0.503	0.500	0.503	0
2	0.499	0.498	0.496	0.60%
3	0.511	0.518	0.508	0.59%
4	0.511	0.512	0.511	0
5	0.555	0.549	0.558	0.54%
6	0.517	0.528	0.514	0.58%
7	0.587	0.566	0.587	0
8	0.556	0.553	0.561	0.90%
9	0.770	0.642	0.775	0.65%
10	0.747	0.631	0.754	0.94%