Determinação via simulação numérica da largura efetiva de lajes de pontes mistas de aço e concreto em seção caixão

Nicoletti, Renato Silva; Souza, Alex Sander Clemente de

Renato Silva Nicoletti

Universidade Federal de São Carlos – UFSCar, Departamento de Engenharia Civil – DECiv, São Carlos, SP, Brasil

https://orcid.org/0000-0002-3021-0944

Alex Sander Clemente de Souza

Universidade Federal de São Carlos – UFSCar, Departamento de Engenharia Civil – DECiv, São Carlos, SP, Brasil

https://orcid.org/0000-0003-3411-0649

Corresponding author: Renato Silva Nicoletti. E-mail: renato_nicoletti@hotmail.com

Conflict of interest: Nothing to declare.

Author contributions: RSN: conceptualization, methodology, numerical analysis, writing; ASCS: formal analysis, methodology, supervision, review.

Editors: Leandro Mouta Trautwein, José Luiz Antunes de Oliveira e Sousa, Guilherme Aris Parsekian.

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Figure 1
Examples of steel-concrete composite box girder bridges. Adapted from Pinho and Bellei [⁵5 F. Pinho and I. H. Bellei, Pontes e Viadutos em Vigas Mistas, 1. ed. Rio de Janeiro: IBS/CBCA, 2007.].

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Figure 2
Displacements due to incompatible deformations. Adapted from Reginato [¹⁶16 L. G. Reginato, “Estudo da largura efetiva de vigas mistas de aço-concreto em carregamento de serviço: método dos elementos finitos versus códigos de projeto,” M.S. thesis, Dep. Eng. Civ., Univ. Fed. Rio Grande do Sul, Porto Alegre, 2017.].

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Figure 3
Effective width concept.

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Figure 2
Displacements due to incompatible deformations. Adapted from Reginato [¹⁶16 L. G. Reginato, “Estudo da largura efetiva de vigas mistas de aço-concreto em carregamento de serviço: método dos elementos finitos versus códigos de projeto,” M.S. thesis, Dep. Eng. Civ., Univ. Fed. Rio Grande do Sul, Porto Alegre, 2017.].

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Figure 3
Effective width concept.

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Figure 4
Relative interface displacement restricted by the Abaqus® [²³23 Abaqus®. Dassault Sistèmes Simulia. Abaqus 6.18. 2016.] “tie constraint” tool.

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Figure 5
Boundary conditions of the models.

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Figure 6
Application of loading models.

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Figure 7
Stress-strain curve of steel (a) and concrete (b). Adapted from Kirchhof [²⁴24 L. D. Kirchhof, “Uma contribuição ao estudo de vigas mistas aço-concreto simplesmente apoiadas em temperatura ambiente e em situação de incêndio,” M.S. thesis, Esc. Eng. São Carlos, Univ. São Paulo, São Carlos, 2004.].

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Figure 8
Detail of the typical mesh of the models.

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Figure 9
Variables for calculating the effective numeric width.

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Figure 10
Stress distribution typical of models in single and double box configurations. [N/mm²].

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Figure 11
Occurrence of maximum normal stresses in the region of the webs in models with simple box configuration.

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Figure 12
Occurrence of maximum normal stresses in the region of the webs in models with double box configuration.

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Figure 13
Effective width versus slab height for single box configuration.

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Figure 14
Effective width versus span length for single box configuration.

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Figure 15
Effective width versus distance between webs for simple box configuration.

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Figure 16
Effective width versus slab height for double box configuration.

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Figure 17
Effective width versus span length for double box configuration.

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Figure 18
Effective width versus distance between girders for double box configuration.

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Figure 9
Variables for calculating the effective numeric width.

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Figure 13
Effective width versus slab height for single box configuration.

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Figure 14
Effective width versus span length for single box configuration.

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Figure 15
Effective width versus distance between webs for simple box configuration.

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Figure 16
Effective width versus slab height for double box configuration.

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Figure 17
Effective width versus span length for double box configuration.

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Figure 18
Effective width versus distance between girders for double box configuration.

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Table 1
Recommendations for calculating the effective width in simply supported beams in buildings.

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Table 2
Materials mechanical properties for parametric study.

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Table 3
Numeric effective width versus slab height for single box configuration.

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Table 4
Relationship between the effective numerical width and the slab height for simple box configuration.

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Table 5
Relationship between the effective numerical width and the longitudinal span length for the simple box configuration.

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Table 6
Relationship between the effective numerical width and the distance between webs for the simple box configuration.

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Table 7
Relationship between the effective numerical width and the slab height for the double box configuration.

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Table 8
Relationship between the effective numerical width and the longitudinal span length for the double box configuration.

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Table 9
Relationship between the effective numerical width and the distance between girders for the double box configuration.

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(1)

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(2)

ABNT NBR 8800 [¹⁵15 Associação Brasileira de Normas Técnicas, Design of Steel and Composite Structures for Buildings, NBR 8800, 2008.]	EN 1994-2-2 [¹⁴14 European Committee for Standardization, Eurocode 4 – Design of Composite Steel and Concrete Structures – Part 2: General Rules and Rules for Bridges, EN 1994-2-2, Brussels, Belgium, 2005.]
The effective width must be less than or equal to:	When the slab extends to both sides of the beam, the effective width must be less than or equal to:
• $\frac{1}{8}$ of the span of the composite beam;	• $\frac{1}{4}$ of the span of the composite beam;
• Half the distance between the center of the analyzed beam and the adjacent beam;	• Average distance between axes of adjacent beams.
• Distance from the center line of the beam to the edge of a cantilevered slab.	In turn, when the slab extends to only one side, the effective width is limited to:
	• $\frac{1}{8}$ of the span of the composite beam;
	• Half the distance between the center of the analyzed beam and the adjacent beam.

MATERIAL	E [MPa]	ν	YIELD STRENGTH [MPa]
Steel	200,000	0.3	229.8
Concrete	30,672.46	0.2	30.0

MODEL	SLAB HEIGHT (h_l) [cm]	EFFECTIVE WIDTH (b_ef) [cm]
1	15.0	201.2
2	20.0	257.8
3	22.5	270.7
4	25.0	289.7
5	27.5	309.3
6	30.0	322.0
7	35.0	325.2
8	50.0	320.9

MODEL	SLAB HEIGHT (h_l) [cm]	EFFECTIVE WIDTH (b_ef) [cm]	$\frac{b_{e f}}{h_{l}}$
1	15.0	201.2	13.42
2	20.0	257.8	12.89
3	22.5	270.7	12.03
4	25.0	289.7	11.59
5	27.5	309.3	11.25
6	30.0	322.0	10.73
*Average*			*11.98*

MODEL	SPAN [cm]	EFFECTIVE WIDTH (b_ef) [cm]	$\frac{S P A N}{b_{e f}}$
9	1000.0	259.9	3.85
10	2000.0	275.5	7.26
11	3000.0	289.7	10.36
12	4000.0	288.8	13.85
13	5000.0	286.5	17.45

MODEL	CANTILEVER [cm]	DISTANCE AMONG WEBS (w) [cm]	EFFECTIVE WIDTH (b_ef) [cm]	$\frac{b_{e f}}{w}$
14	350.0	580.0	216.3	0.37
15	340.0	600.0	205.0	0.34
16	330.0	620.0	192.4	0.31
17	320.0	640.0	174.0	0.27
18	310.0	660.0	130.9	0.20
19	300.0	680.0	124.0	0.18
*Average*				*0.28*

MODEL	SLAB HEIGHT (h_l) [cm]	EFFECTIVE WIDTH (b_ef) [cm]	$\frac{b_{e f}}{h_{l}}$
20	15.0	210.7	14.05
21	20.0	215.3	10.77
22	22.5	217.4	9.66
23	25.0	223.1	8.92
24	27.5	224.5	8.16
25	30.0	219.1	7.30
*Average*			*9.81*

MODEL	SPAN [cm]	EFFECTIVE WIDTH (b_ef) [cm]	$\frac{S P A N}{b_{e f}}$
26	1,000.0	248.4	4.03
27	2,000.0	275.5	7.26
28	3,000.0	277.1	10.83
29	4,000.0	277.9	14.39
30	5,000.0	279.2	17.91

MODEL	DISTANCE BETWEEN GIRDERS (a) [cm]	EFFECTIVE WIDTH (b_ef) [cm]	$\frac{b_{e f}}{a}$
31	580.0	255.7	0.44
32	600.0	249.4	0.42
33	620.0	235.2	0.38
34	640.0	217.4	0.34
35	660.0	213.3	0.32
*Average*			*0.38*

[1] Corresponding author: Renato Silva Nicoletti. E-mail: renato_nicoletti@hotmail.com

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Determinação via simulação numérica da largura efetiva de lajes de pontes mistas de aço e concreto em seção caixão

RESUMO: