Probabilistic models for live loads in buildings: critical review, comparison to Brazilian design standards and calibration of partial safety factors

Costa, Luis Gustavo Lopes; Santiago, Wagner Carvalho; Beck, André Teófilo

doi:10.1590/S1983-41952023000200004

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Revista IBRACON de Estruturas e Materiais

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ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 16 (2) • 2023 • https://doi.org/10.1590/S1983-41952023000200004 copy

Probabilistic models for live loads in buildings: critical review, comparison to Brazilian design standards and calibration of partial safety factors

Modelos probabilísticos para a ação de utilização em edifícios: análise crítica, comparação com normas brasileiras de projeto, e calibração dos fatores parciais de segurança

Authorship SCIMAGO INSTITUTIONS RANKINGS

abstract:

Nowadays, structural “limit state” design is made using characteristic or nominal values of actions, partial safety factors and load combination factors. The actual loading that a structure will be subjected to throughout its life is not known at the design phase. Yet, probabilistic models of such loadings are useful for the rational determination of partial safety factors and load combination factors. The probabilistic model leading to nominal live loads of NBR 6120:2019 (Design Loads for Structures) has never been openly discussed. Herein a simple probabilistic model describing spatial and temporal variabilities of live loads in buildings is presented and discussed. The model is built as a sum of two stochastic processes representing the sustained and intermittent parts of the live load. Model parameters are the ones recommended by the Joint Committee on Structural Safety (JCSS), based on extensive surveys done in several countries. By way of Monte Carlo simulations, sample values of live load actions are obtained for buildings of different occupancy types. These values are compared with those recommended by international standards, and those recommended in NBR 6120:2019 and NBR 8681:2003 (Actions and Safety of Structures). The corresponding statistics for the fifty-year extreme and arbitrary point-in-time distributions of live loads are presented; these statistics are very relevant for reliability analyses and for reliability-based code calibration. The stochastic live load model is also employed in a reliability-based calibration to obtain partial safety factors and load combination factors to be used in Brazilian design codes, for ultimate and serviceability limit state verifications.

Keywords:
live load model; probabilistic model; structural reliability; partial safety factor; load combination factor; NBR 8681; NBR 6120

Occupancy type	$A_{0}$ (m²)	Sustained load				Extraordinary load				Reference
Occupancy type	$A_{0}$ (m²)	$m_{q}$ (kPa)	$σ_{V, q}$ (kPa)	$σ_{U, q}$ (kPa)	$1 / λ_{q}$ (years)	$m_{p}$ (kPa)	$σ_{U, p}$ (kPa)	$1 / λ_{p}$ (years)	$d_{p}$ (days)	Reference
Office	20	0.50	0.30	0.60	5	0.20	0.40	0.3	1–3	JCSS [²⁷27 Joint Committee on Structural Safety, Probabilistic Model Code – Part 2: Load Models. 2001. [Online]. Available: https://www.jcss-lc.org/jcss-probabilistic-model-code/ https://www.jcss-lc.org/jcss-probabilist... ]
Residence	20	0.30	0.15	0.30	7	0.20	0.30	1.0	1–3	JCSS [²⁷27 Joint Committee on Structural Safety, Probabilistic Model Code – Part 2: Load Models. 2001. [Online]. Available: https://www.jcss-lc.org/jcss-probabilistic-model-code/ https://www.jcss-lc.org/jcss-probabilist... ]
Hotel room	20	0.30	0.05	0.10	10	0.20	0.40	0.1	1–3	JCSS [²⁷27 Joint Committee on Structural Safety, Probabilistic Model Code – Part 2: Load Models. 2001. [Online]. Available: https://www.jcss-lc.org/jcss-probabilistic-model-code/ https://www.jcss-lc.org/jcss-probabilist... ]
Patient room	20	0.40	0.30	0.60	5–10	0.20	0.40	1.0	1–3	JCSS [²⁷27 Joint Committee on Structural Safety, Probabilistic Model Code – Part 2: Load Models. 2001. [Online]. Available: https://www.jcss-lc.org/jcss-probabilistic-model-code/ https://www.jcss-lc.org/jcss-probabilist... ]
Classroom	100	0.60	0.15	0.40	10	0.20	0.40	0.3	1–5	Honfi [⁴¹41 D. Honfi, "Serviceability floor loads," Struct. Saf., vol. 50, pp. 27–38, 2014., http://dx.doi.org/10.1016/j.strusafe.2014.03.004. http://dx.doi.org/10.1016/j.strusafe.201... ]
Retail	100	0.90	0.60	0.60	1–5	0.40	0.60	1.0	1–14	Costa [⁴²42 L. G. L. Costa, “Modelos probabilísticos para ações variáveis brasileiras,” M.S. thesis, São Carlos Sch. Eng., Univ. São Paulo, São Carlos, 2023 [in preparation].]

Test	Statistic	P-value
Anderson-Darling	0.2482592	0.9713050
Kolgomorov-Smirnov	0.0056237	0.9098539
Pearson $χ^{2}$	70.272	0.7479799

Case	Description
I	Lifetime maximum sustained load + maximum extraordinary load during that tenancy
II	Lifetime maximum extraordinary load + corresponding instantaneous sustained load
III	Simultaneous occurrence of lifetime maxima for both sustained and extraordinary loads
IV	Combination where the neither the sustained nor the extraordinary loads are at their maximum values

Occupancy type	$L_{n}$ ^* (kN/m²)	$A_{r e f}$ (m²)	$L_{a p t}$ (Gamma)		$L_{50}$ (Gumbel)		$L_{140}$ (Gumbel)		$γ_{L}$	$ψ_{0}$
Occupancy type	$L_{n}$ ^* (kN/m²)	$A_{r e f}$ (m²)	$μ$	c.o.v.	$μ$	c.o.v.	$μ$	c.o.v.	$γ_{L}$	$ψ_{0}$
Office	2.5	110	0.20 $L_{n}$	0.94	0.93 $L_{n}$	0.26	1.11 $L_{n}$	0.21	1.56	0.42
Residence	1.5	140	0.20 $L_{n}$	0.75	0.93 $L_{n}$	0.22	1.09 $L_{n}$	0.18	1.48	0.52
Hotel room	1.5	220	0.20 $L_{n}$	0.24	0.95 $L_{n}$	0.14	1.05 $L_{n}$	0.13	1.31	0.67
Patient room	2.0	110	0.20 $L_{n}$	1.16	0.89 $L_{n}$	0.35	1.13 $L_{n}$	0.28	1.72	0.42
Classroom	3.0	300	0.20 $L_{n}$	0.61	0.92 $L_{n}$	0.24	1.09 $L_{n}$	0.20	1.52	0.53
Retail	4.0	310	0.22 $L_{n}$	0.86	0.92 $L_{n}$	0.28	1.11 $L_{n}$	0.22	1.59	0.40
Average			0.21 $L_{n}$	0.76	0.92 $L_{n}$	0.25	–	–	1.53	0.49
Santiago et al. [⁴⁷47 W. C. Santiago, H. M. Kroetz, S. H. C. Santos, F. R. Stucchi, and A. T. Beck, "Reliability-based calibration of main brazilian structural design codes," Lat. Am. J. Solids Struct., vol. 17, no. 1, e245, 2020.]			0.25 $L_{n}$	0.55	1.00 $L_{n}$	0.40	–	–
Ellingwood et al. [³²32 B. Ellingwood, T. V Galambos, J. G. MacGregor, and C. A. Cornell, Development of a Probability Based Load Criterion for American National Standard A58 (Spec. Publ. 577). Washington, DC, USA: US Dept. Commer., Nat. Bur. Stand., Jun. 1980.]			0.25 $L_{n}$	0.55	1.00 $L_{n}$	0.25	–	–
Szerszen and Nowak [⁵⁰50 M. M. Szerszen and A. S. Nowak, "Calibration of design code for buildings (ACI 318): Part 2 – reliability analysis and resistance factors," ACI Struct. J., vol. 100, no. 3, pp. 383–391, 2003, http://dx.doi.org/10.14359/12614. http://dx.doi.org/10.14359/12614... ]			–	–	0.93 $L_{n}$	0.18	–	–
Holický and Sýkora [⁵¹51 M. Holický and M. Sýkora, “Conventional probabilistic models for calibration of codes,” in Proc. 11th Int. Conf. Appl. Statist. Probab. Civ. Eng., M. H. Faber, J. Köhler and K. Nishijima, Eds. Zurich, Switzerland: CRC Press, 2011, pp. 969–976.]			–	–	0.60 $L_{n}$	0.35	–	–

Coefficient	Before calibration NBR 8800:2008 [⁴⁵45 Associação Brasileira de Normas Técnicas, Design of Steel and Composite Structures for Buildings, ABNT NBR 8800, 2008, 237 p.]	Before calibration NBR 6118:2014 [⁴⁶46 Associação Brasileira de Normas Técnicas, Design of Concrete Structures – Procedure, ABNT NBR 6118, 2014, 238 p.]	Original calibration [⁴⁷47 W. C. Santiago, H. M. Kroetz, S. H. C. Santos, F. R. Stucchi, and A. T. Beck, "Reliability-based calibration of main brazilian structural design codes," Lat. Am. J. Solids Struct., vol. 17, no. 1, e245, 2020.] $β_{T} = 3.0$	New calibration^† $β_{T} = 3.17$
$γ_{C}$	$-$	1.40	1.40	1.40
$γ_{S}$	$-$	1.15	1.15	1.15
$γ_{a 1}$	1.10	$-$	1.10	1.10
$γ_{a 2}$	1.35	$-$	1.30	1.40
$γ_{D}$	1.25	1.40	1.25	1.20^⅋
$γ_{L}$	1.50	1.40	1.70	1.50
$γ_{W}$	1.40	1.40	1.65	1.50
$ψ_{L}$	0.50 / 0.70 / 0.80	0.50 / 0.70 / 0.80	0.35	0.45
$ψ_{W}$	0.60	0.60	0.30	0.35
$γ_{L} ∙ ψ_{L}$ *	0.75 / 1.05 / 1.20	0.70 / 0.98 / 1.12	0.60	0.68
$γ_{W} ∙ ψ_{W}$ *	0.84	0.84	0.50	0.53

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[1] Corresponding author: André Teófilo Beck. E-mail: atbeck@sc.usp.br