Dynamic analysis of floors subjected to rhythmic human activities based on the use of biodynamic models: numerical and experimental modelling

Sousa, Felipe Almeida de; Debona, Gilvan Lunz; Silva, José Guilherme Santos da

doi:10.1590/S1983-41952024000400002

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ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 17 (4) • 2024 • https://doi.org/10.1590/S1983-41952024000400002 copy

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10.1590/S1983-41952024000400011

Dynamic analysis of floors subjected to rhythmic human activities based on the use of biodynamic models: numerical and experimental modelling

Análise dinâmica de pisos submetidos a atividades humanas rítmicas com base no uso de modelos biodinâmicos: modelagem numérica e experimental

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

This work aims the assessment of the dynamic structural response of reinforced concrete floors subjected to rhythmic human activities, based on the use of biodynamic models, in order to consider the people-structure interaction effect. Initially, an experimental modal analysis on the investigated floor , with dimensions of 16m x 35m, was performed, in order to identify and assess the global dynamic behaviour of the structure. In sequence, a finite element model was developed and calibrated through experimental results. After that, based on forced vibration analyses, the floor dynamic response was determined (displacements and accelerations). It is concluded that the biodynamic systems modelling induced significant attenuations on the structural response when compared to those calculated based on the use of traditional “only force” models.

Keywords:
concrete floors; biodynamic systems; experimental dynamics; rhythmic human activities; human comfort assessment

Excitation	1º jump	2º jump	3º jump	4º jump	5º jump	Mean value
Structural damping	2.75%	2.82%	2.80%	2.77%	2.73%	2.77%

Tests	Natural Frequency (Hz)
Tests	Experimental Tests	Finite Element Model	Differences (%)
II	f_exp= 7.80 Hz	f₀₃ = 8.00 Hz	2.56
III	f_exp= 8.05 Hz	f₀₃ = 8.00 Hz	0.62

Person	Mass (kg)	Damping (Ns/m)	Stiffness (N/m)	Pearson’s Correlation (F_d1 x F_d)
1	92.70	820.94	42812.81	0.98
2	81.95	657.02	37521.26	0.97
3	67.80	547.48	34311.23	0.99
4	56.40	589.41	39755.25	0.95
5	57.60	1019.22	42314.31	0.95
6	81.00	1806.75	29018.39	0.97
7	69.70	645.85	38085.19	0.98
8	88.55	636.79	40037.26	0.99
9	64.80	768.36	37653.04	0.97
10	68.65	678.62	43094.19	0.98

SS	Biodynamic [¹1 F. A. de Sousa, "Análise da resposta estrutural dinâmica de pisos de edifícios submetidos a atividades humanas rítmicas com base no emprego de sistemas biodinâmicos," DSc Thesis (In development). Civ. Eng. Postgraduate Programme (PGECIV). State Univ. Rio de Janeiro (UERJ), Rio de Janeiro, RJ, Brazil, 2023.]			Faisca [⁷7 R. G. Faisca, "Caracterização de cargas dinâmicas geradas por atividades humanas", DSc Thesis, Civil Engineering Postgraduate Programme (UFRJ), Rio de Janeiro, RJ, Brazil, 2003.]			AISC [³3 T. M. Murray, D. E. Allen, E. E. Ungar, and D. B. Davis, Steel Design Guide 11: Vibration of Steel-Frame Structural Systems Due to Human Activities, 2nd ed., Chicago: American Institute of Steel Construction, 2016]			SCI [⁶6 A. Smith, S. Hick, and P. Devine, Design of Floors for Vibration: A New Approach (SCI Publication), Ascot, UK: The Steel Construction Institute (SCI), 2009. https://doi.org/10.13140/RG.2.2.29342.95048. https://doi.org/10.13140/RG.2.2.29342.95... ]
SS	a_p	a_w,_rms	VDV	a_p	a_w,_rms	VDV	a_p	a_w,_rms	VDV	a_p	a_w,_rms	VDV
A	0.102	0.031	0.072	0.122	0.083	0.163	0.665	0.176	0.476	0.424	0.168	0.399
B	0.103	0.033	0.076	0.122	0.083	0.163	0.487	0.168	0.425	0.293	0.166	0.378
C	0.024	0.009	0.021	0.017	0.012	0.027	0.302	0.200	0.400	0.153	0.040	0.133
D	0.008	0.003	0.008	0.008	0.002	0.007	0.130	0.088	0.174	0.082	0.013	0.051
E	0.010	0.002	0.005	0.004	0.001	0.002	0.070	0.047	0.094	0.034	0.005	0.021
F	0.004	0.001	0.003	0.002	0.000	0.001	0.035	0.024	0.048	0.017	0.003	0.011

SS	Biodynamic [¹1 F. A. de Sousa, "Análise da resposta estrutural dinâmica de pisos de edifícios submetidos a atividades humanas rítmicas com base no emprego de sistemas biodinâmicos," DSc Thesis (In development). Civ. Eng. Postgraduate Programme (PGECIV). State Univ. Rio de Janeiro (UERJ), Rio de Janeiro, RJ, Brazil, 2023.]			Faisca [⁷7 R. G. Faisca, "Caracterização de cargas dinâmicas geradas por atividades humanas", DSc Thesis, Civil Engineering Postgraduate Programme (UFRJ), Rio de Janeiro, RJ, Brazil, 2003.]			AISC [³3 T. M. Murray, D. E. Allen, E. E. Ungar, and D. B. Davis, Steel Design Guide 11: Vibration of Steel-Frame Structural Systems Due to Human Activities, 2nd ed., Chicago: American Institute of Steel Construction, 2016]			SCI [⁶6 A. Smith, S. Hick, and P. Devine, Design of Floors for Vibration: A New Approach (SCI Publication), Ascot, UK: The Steel Construction Institute (SCI), 2009. https://doi.org/10.13140/RG.2.2.29342.95048. https://doi.org/10.13140/RG.2.2.29342.95... ]
SS	a_p	a_w,_rms	VDV	a_p	a_w,_rms	VDV	a_p	a_w,_rms	VDV	a_p	a_w,_rms	VDV
A	0.003	0.001	0.002	0.002	0.000	0.001	0.035	0.024	0.048	0.017	0.003	0.011
B	0.004	0.001	0.003	0.004	0.001	0.002	0.071	0.047	0.093	0.033	0.005	0.021
C	0.009	0.003	0.007	0.009	0.002	0.007	0.138	0.094	0.186	0.088	0.014	0.055
D	0.027	0.008	0.018	0.016	0.011	0.025	0.280	0.187	0.373	0.145	0.037	0.124
E	0.099	0.030	0.070	0.119	0.081	0.159	0.472	0.163	0.414	0.284	0.161	0.368
F	0.109	0.034	0.079	0.122	0.083	0.163	0.665	0.176	0.476	0.424	0.168	0.399

SS	Biodynamic [¹1 F. A. de Sousa, "Análise da resposta estrutural dinâmica de pisos de edifícios submetidos a atividades humanas rítmicas com base no emprego de sistemas biodinâmicos," DSc Thesis (In development). Civ. Eng. Postgraduate Programme (PGECIV). State Univ. Rio de Janeiro (UERJ), Rio de Janeiro, RJ, Brazil, 2023.]			Faisca [⁷7 R. G. Faisca, "Caracterização de cargas dinâmicas geradas por atividades humanas", DSc Thesis, Civil Engineering Postgraduate Programme (UFRJ), Rio de Janeiro, RJ, Brazil, 2003.]			AISC [³3 T. M. Murray, D. E. Allen, E. E. Ungar, and D. B. Davis, Steel Design Guide 11: Vibration of Steel-Frame Structural Systems Due to Human Activities, 2nd ed., Chicago: American Institute of Steel Construction, 2016]			SCI [⁶6 A. Smith, S. Hick, and P. Devine, Design of Floors for Vibration: A New Approach (SCI Publication), Ascot, UK: The Steel Construction Institute (SCI), 2009. https://doi.org/10.13140/RG.2.2.29342.95048. https://doi.org/10.13140/RG.2.2.29342.95... ]
SS	a_p	a_w,_rms	VDV	a_p	a_w,_rms	VDV	a_p	a_w,_rms	VDV	a_p	a_w,_rms	VDV
A	0.010	0.004	0.011	0.015	0.002	0.008	0.180	0.134	0.266	0.107	0.018	0.069
B	0.024	0.009	0.021	0.039	0.012	0.027	0.341	0.239	0.477	0.214	0.040	0.129
C	0.110	0.035	0.080	0.131	0.086	0.168	0.865	0.467	0.978	0.371	0.170	0.389
D	0.083	0.029	0.068	0.123	0.081	0.158	0.821	0.436	0.916	0.349	0.160	0.366
E	0.023	0.008	0.018	0.037	0.011	0.025	0.340	0.239	0.477	0.221	0.038	0.130
F	0.008	0.003	0.009	0.015	0.002	0.008	0.180	0.134	0.266	0.107	0.018	0.069

a_w,_rms (m/s²) [⁶6 A. Smith, S. Hick, and P. Devine, Design of Floors for Vibration: A New Approach (SCI Publication), Ascot, UK: The Steel Construction Institute (SCI), 2009. https://doi.org/10.13140/RG.2.2.29342.95048. https://doi.org/10.13140/RG.2.2.29342.95... ]	VDV (m/s^1.75) [³³33 M. Setareh, "Evaluation and assessment of vibrations owing to human activity," Proc. Inst. Civ. Eng., Struct. Build., vol. 165, no. 5, pp. 219-231, 2012.]	VDV (m/s^1.75) [¹¹11 J. T. Littler and B. R. Ellis, "The response of grandstands to dynamic crowd loads," Proc. Inst. Civ. Eng., Struct. Build., vol. 140, pp. 355-365, 2000, http://dx.doi.org/10.1680/stbu.2000.140.4.355. http://dx.doi.org/10.1680/stbu.2000.140.... ]	Person’s reaction
< 0.35	< 0.50	< 0.66	Reasonable: passive people
0.35 - 1,27	0.50 - 3.50	0.66 - 2.38	Disturbing
1.27 - 2.47	3.50 - 6.90	2.38 - 4.64	Unacceptable
> 2.47	> 6.90	> 4.64	Probably causing panic

Load model	a_p (m/s²)	a_w,rms (m/s²)	VDV (m/s^1.75)	SS
LM I	0.665	0.176	0.476	Section A
LM II	0.865	0.467	0.978	Section C
LM III	0.665	0.176	0.476	Section F

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[1] Corresponding author: José Guilherme Santos da Silva. E-mail: jgss@uerj.br