Statistical analysis of second order effects variation with the stories height of reinforced concrete buildings

In this paper the simplified method to evaluate final efforts using γ_z coefficient is studied considering the variation of the second order effects with the height of the buildings. With this purpose, several reinforced concrete buildings of medium height are analyzed in first and second order using ANSYS software. Initially, it was checked that the (_z coefficient should be used as magnifier of first order moments to evaluate final second order moments. Therefore, the study is developed considering the relation (final second order moments/ first order moments), calculated for each story of the structures. This moments relation is called magnifier of first order moments, "γ", and, in the ideal situation, it must coincide with the γ_z value. However, it is observed that the reason γ /γ_z varies with the height of the buildings. Furthermore, using an statistical analysis, it was checked that γ /γ_z relation is generally lower than 1.05 and varies significantly in accordance with the considered building and with the presence or not of symmetry in the structure.

Keywords:
reinforced concrete; second order effects; (_z coefficient

Authorship

D.M. OLIVEIRA

Universidade Federal de Minas Gerais, Escola de Engenharia, Deptº de Engenharia de Materiais e Construção, Belo Horizonte, MG, Brasil; danielle@demc.ufmg.br, ccrstar@demc.ufmg.br, sidnea@ufmg.br Universidade Federal de Minas GeraisBrazilBelo Horizonte, MG, BrazilUniversidade Federal de Minas Gerais, Escola de Engenharia, Deptº de Engenharia de Materiais e Construção, Belo Horizonte, MG, Brasil; danielle@demc.ufmg.br, ccrstar@demc.ufmg.br, sidnea@ufmg.br

N.A. SILVA

Universidade Federal de Minas Gerais, Escola de Engenharia, Deptº de Engenharia de Estruturas, Belo Horizonte, MG, Brasil; ney@dees.ufmg.brUniversidade Federal de Minas GeraisBrazilBelo Horizonte, MG, BrazilUniversidade Federal de Minas Gerais, Escola de Engenharia, Deptº de Engenharia de Estruturas, Belo Horizonte, MG, Brasil; ney@dees.ufmg.br

C.C. RIBEIRO

S.E.C. RIBEIRO

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables | Formulas

Figures (7)
Tables (7)
Formulas (13)

Building	Nº of Stories	Ceiling height (m)	Nº of Slabs	Nº of Beams	Nº of Columns	f_ck (MPa)
I	16	2.90	8	8	15	20
II	18	2.55	11	21	16	30
III	20	2.75	9	10	15	45
IV	30	2.85	4	6	9	20
V	22	2.75	11	20	22	65
VI	15	2.90	9	8	16	25
VII	18	2.88	10	11	16	25
VIII	18	2.70	17	31	28	25
IX	20	2.56	12	27	14	30
X	20	2.90	6	9	12	25

Building	Direction	γ_z	Classification
I	X	1.19	Sway structure
I	Y	1.14	Sway structure
II	X	1.32	Sway structure
II	Y	1.16	Sway structure
III	X	1.06	Non-sway structure
III	Y	1.32	Sway structure
IV	X = Y	1.30	Sway structure
V	X	1.17	Sway structure
V	Y	1.28	Sway structure
VI	X = Y	1.21	Sway structure
VII	X	1.27	Sway structure
VII	Y	1.14	Sway structure
VIII	X	1.30	Sway structure
VIII	Y	1.22	Sway structure
IX	X	1.31	Sway structure
IX	Y	1.29	Sway structure
X	X	1.30	Sway structure
X	Y	1.22	Sway structure

Building	Direction	Columns		Beams
Building	Direction	Axial Force	Bending Moment	Shear Force	Bending Moment
I	X	1.01	1.15	1.01	1.08
I	Y	1.01	1.14	1.02	1.05
II	X	1.01	1.22	1.02	1.29
II	Y	1.02	1.12	1.03	1.20
III	X	1.02	1.11	1.02	1.03
III	Y	1.02	1.18	1.03	1.24
IV	X = Y	1.03	1.15	1.03	1.18
V	X	1.02	1.14	1.03	1.14
V	Y	1.03	1.17	1.00	1.19
VI	X = Y	1.02	1.09	1.03	1.14
VII	X	1.02	1.14	1.04	1.20
VII	Y	1.03	1.11	1.04	1.13
VIII	X	1.02	1.17	1.03	1.33
VIII	Y	1.02	1.16	1.02	1.17
IX	X	1.01	1.25	1.02	1.28
IX	Y	1.01	1.19	1.03	1.20
X	X	1.02	1.16	1.01	1.22
X	Y	1.02	1.11	1.03	1.16

Variable	Sample size (n)	Mean	Standard Deviation	Coefficient of Variation (%)	Minimum	Median	Maximum
γ / γz Columns	349	0.988	0.060	6.120	0.780	0.990	1.140
γ / γz Beams	349	0.975	0.065	6.720	0.770	0.970	1.140

Item	Columns	Beams
H	30.005	48.386
χ²0,05,9	16.92	16.92
p	0.000	0.000
(	0.05	0.05
Conclusion	H0 Rejected	H0 Rejected