Comparative analysis of design models for concrete corbels

The main objective of this paper is performing a comparative analysis of some design models for precast concrete corbels. For this, it was analyzed design models from Brazilian (NBR 9062) and European (EUROCODE 2) Codes and a US design handbook (PCI). Moreover, three analytical models showed in the literature are analyzed. The objective of this comparative is identifying the best design models to represent the failure load of concrete corbels by the tie yields or by the concrete crushing. Moreover, it is intended to evaluate the contribution of horizontal stirrups to resistance of concrete corbels. For this, a database was assembled from test results of concrete corbels carried out by several researchers and they are showed in the literature. The design models were applied to this database and from statistical tools, adjustments coefficients are recommended to be applied on these design models to take into account the results dispersion found in the analysis.

Keywords :
corbels; precast concrete; design models; horizontal stirrup

Authorship

D. L. Araújo

Universidade Federal de Goiás, Goiânia, GO, Brasil. dlaraujo@ufg.br, antonioneto117@hotmail.com, faustinhoalobo@gmail.comUniversidade Federal de GoiásBrazilGoiânia, GO, BrazilUniversidade Federal de Goiás, Goiânia, GO, Brasil. dlaraujo@ufg.br, antonioneto117@hotmail.com, faustinhoalobo@gmail.com

A. P. Silva Neto

F. A. Lobo

M. K. El Debs

Universidade de São Paulo, São Carlos, SP, Brasil. mkdebs@sc.usp.brUniversidade de São PauloBrazilSão Carlos, SP, BrazilUniversidade de São Paulo, São Carlos, SP, Brasil. mkdebs@sc.usp.br

SCIMAGO INSTITUTIONS RANKINGS

Universidade de São Paulo, São Carlos, SP, Brasil. mkdebs@sc.usp.brUniversidade de São PauloBrazilSão Carlos, SP, BrazilUniversidade de São Paulo, São Carlos, SP, Brasil. mkdebs@sc.usp.br

Figures | Tables | Formulas

Figures (9)
Tables (4)
Formulas (44)

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Figure 1
(a) Truss geometry and (b) width of strut from the ABNT NBR 9062 ^[1][1] ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS - ABNT. NBR 9062: Design and execution of precast concrete structures. Rio de Janeiro, 2006 (In Portuguese). design method

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Figure 2
(a) Truss geometry of EUROCODE 2 ^[2][2] COMITÉ EUROPÉEN DE NORMALISATION. EUROCODE 2: Design of concrete structures - Part 1.1: General rules and rules for buildings. Brussels, Belgium, 2004. and (b) simplified geometry

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Figure 3
(a) Truss geometry of the PCI ^[3][3] PRECAST/PRESTRESSED CONCRETE INSTITUTE - PCI. PCI Design Handbook. 7th Edition, 2010. design method and (b) adapting for a double corbel

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Figure 4
Fernandes and El Debs ^[4][4] FERNANDES, R. M.; EL DEBS, M. K. Análise da capacidade resistente de consolos de concreto armado considerando a contribuição da armadura de costura. Cadernos de Engenharia de Estruturas, São Carlos, v.7, n.25, 2005; p.103‒128 (In Portuguese). analytical method based on the method presented by Leonhardt e Mönnig ^[5][5] LEONHARDT, F.; MÖNNIG, E. Construções de concreto: Casos especiais de dimensionamento de estruturas de concreto armado. v.2.1., Rio de Janeiro: Interciência, 1978 (In Portuguese).

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Figure 5
Hagberg ^[6][6] HAGBERG, T. Design of concrete brackets: on the application of the truss analogy. ACI Journal, v.80, n.1, 1983; p.3‒12. analytical method

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Figure 6
Campione et al. ^[7][7] CAMPIONE, G.; LA MENDOLA, L.; PAPIA, M. Flexural behaviour of concrete corbels containing fibers or wrapped with FRP sheets. Materials and Structures, v.38, 2005; p.617‒625. analytical method

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Figure 7
(a) Estimated failure load from tension tie and (b) compressive strut on a hypothetical corbel

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Figure 8
Comparison of design methods with experimental results of database

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Figure 9
Comparison of analytical methods with experimental results of database

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Table 1
Comparison of design methods with experimental results of database (F _exp /F _calc )

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Table 2
Comparison of analytical methods with experimental results of database (F _exp /F _calc )

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Table 4
Values of the coefficient ϕ for methods when failure occurs on compressive strut

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Table 3
Values of the coefficient ϕ for methods when failure occurs on tension tie

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Figure 1 (a) Truss geometry and (b) width of strut from the ABNT NBR 9062 ^[1][1] ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS - ABNT. NBR 9062: Design and execution of precast concrete structures. Rio de Janeiro, 2006 (In Portuguese). design method

Figure 2 (a) Truss geometry of EUROCODE 2 ^[2][2] COMITÉ EUROPÉEN DE NORMALISATION. EUROCODE 2: Design of concrete structures - Part 1.1: General rules and rules for buildings. Brussels, Belgium, 2004. and (b) simplified geometry

Figure 3 (a) Truss geometry of the PCI ^[3][3] PRECAST/PRESTRESSED CONCRETE INSTITUTE - PCI. PCI Design Handbook. 7th Edition, 2010. design method and (b) adapting for a double corbel

Figure 4 Fernandes and El Debs ^[4][4] FERNANDES, R. M.; EL DEBS, M. K. Análise da capacidade resistente de consolos de concreto armado considerando a contribuição da armadura de costura. Cadernos de Engenharia de Estruturas, São Carlos, v.7, n.25, 2005; p.103‒128 (In Portuguese). analytical method based on the method presented by Leonhardt e Mönnig ^[5][5] LEONHARDT, F.; MÖNNIG, E. Construções de concreto: Casos especiais de dimensionamento de estruturas de concreto armado. v.2.1., Rio de Janeiro: Interciência, 1978 (In Portuguese).

Figure 5 Hagberg ^[6][6] HAGBERG, T. Design of concrete brackets: on the application of the truss analogy. ACI Journal, v.80, n.1, 1983; p.3‒12. analytical method

Figure 6 Campione et al. ^[7][7] CAMPIONE, G.; LA MENDOLA, L.; PAPIA, M. Flexural behaviour of concrete corbels containing fibers or wrapped with FRP sheets. Materials and Structures, v.38, 2005; p.617‒625. analytical method

Figure 7 (a) Estimated failure load from tension tie and (b) compressive strut on a hypothetical corbel

Figure 8 Comparison of design methods with experimental results of database

Figure 9 Comparison of analytical methods with experimental results of database

Table 1 Comparison of design methods with experimental results of database (F _exp /F _calc )

Table 2 Comparison of analytical methods with experimental results of database (F _exp /F _calc )

Table 4 Values of the coefficient ϕ for methods when failure occurs on compressive strut

Table 3 Values of the coefficient ϕ for methods when failure occurs on tension tie



Method	Corbels without horizontal stirrups	Corbels with horizontal stirrups
ABNT NBR 9062 ^[1][1] ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS - ABNT. NBR 9062: Design and execution of precast concrete structures. Rio de Janeiro, 2006 (In Portuguese).	0.980 1.357
PCI ^[3][3] PRECAST/PRESTRESSED CONCRETE INSTITUTE - PCI. PCI Design Handbook. 7th Edition, 2010.	1.140 1.481
EUROCODE 2 ^[2][2] COMITÉ EUROPÉEN DE NORMALISATION. EUROCODE 2: Design of concrete structures - Part 1.1: General rules and rules for buildings. Brussels, Belgium, 2004.	1.329 1.590
Hagberg ^[6][6] HAGBERG, T. Design of concrete brackets: on the application of the truss analogy. ACI Journal, v.80, n.1, 1983; p.3‒12.	- 1.106
Fernandes and El Debs ^[4][4] FERNANDES, R. M.; EL DEBS, M. K. Análise da capacidade resistente de consolos de concreto armado considerando a contribuição da armadura de costura. Cadernos de Engenharia de Estruturas, São Carlos, v.7, n.25, 2005; p.103‒128 (In Portuguese).	- 1.022
Campione et al. ^[7][7] CAMPIONE, G.; LA MENDOLA, L.; PAPIA, M. Flexural behaviour of concrete corbels containing fibers or wrapped with FRP sheets. Materials and Structures, v.38, 2005; p.617‒625.	0.738 0.691

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Comparative analysis of design models for concrete corbels

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