Resultados experimentais e análise de carga limite pelo Método de Bielas e Tirantes (MBT) de vigas-parede com entalhes e aberturas

Abreu Neta, Izabel Castro de; Miranda, Antonio Carlos de Oliveira; Lameiras, Rodrigo de Melo; Leite, Carlos Henrique de Oliveira

Izabel Castro de Abreu Neta

conceptualization

tests experimental

STM construction

analysis

data curation

writing

Universidade de Brasília - UNB, Departamento de Engenharia Civil e Ambiental, Brasília, DF, Brasil

http://orcid.org/0000-0002-5933-975X

Antonio Carlos de Oliveira Miranda

supervision

funding acquisition

conceptualization

Universidade de Brasília - UNB, Departamento de Engenharia Civil e Ambiental, Brasília, DF, Brasil

http://orcid.org/0000-0002-5225-7428

Rodrigo de Melo Lameiras

supervision

funding acquisition

conceptualization

Universidade de Brasília - UNB, Departamento de Engenharia Civil e Ambiental, Brasília, DF, Brasil

http://orcid.org/0000-0003-3804-9427

Carlos Henrique de Oliveira Leite

conceptualization

tests experimental

STM construction

analysis

data curation

writing

Universidade de Brasília - UNB, Departamento de Engenharia Civil e Ambiental, Brasília, DF, Brasil

http://orcid.org/0000-0002-9972-3641

Corresponding author: Izabel Castro de Abreu Neta. E-mail: izabel.castroa@gmail.com

Conflict of interest: Nothing to declare.

Editors: Samir Maghous

Daniel Carlos Taissum Cardoso

Thumbnail

Figure 1
Deep beam geometries (dimensions in mm)

Thumbnail

Figure 2
Details of reinforcements on DB-NR-H1 (dimensions in mm)

Thumbnail

Figure 5
Details of reinforcements on DB-WR-H2 (dimensions in mm)

Thumbnail

Figure 3
Details of reinforcements on DB-WR-H1 (dimensions in mm)

Thumbnail

Figure 4
Details of reinforcements on DB-NR-H2 (dimensions in mm)

Thumbnail

Figure 6
Test setup.

Thumbnail

Figure 2
Details of reinforcements on DB-NR-H1 (dimensions in mm)

Thumbnail

Figure 5
Details of reinforcements on DB-WR-H2 (dimensions in mm)

Thumbnail

Figure 3
Details of reinforcements on DB-WR-H1 (dimensions in mm)

Thumbnail

Figure 4
Details of reinforcements on DB-NR-H2 (dimensions in mm)

Thumbnail

Figure 6
Test setup.

Thumbnail

Figure 7
Comparison of average failure loads

Thumbnail

Figure 8
Comparison between cracking loads and failure loads

Thumbnail

Figure 9
Cracking pattern in DB-NR-H1 (load in kN): (a) 85% of P_f ; (b) 95% of P_f ; (c) Failure.

Thumbnail

Figure 16
Cracking pattern in DB-WR-H2-NA-2 (load in kN): (a) 30% of P_f ; (b) 50% of P_f ; (c) 70% of P_f ; (d) 90% of P_f ; (e) Failure.

Thumbnail

Figure 10
Cracking pattern in DB-NR-H1-2 (load in kN): (a) 85% of P_f ; (b) 95% of P_f ; (c) Failure.

Thumbnail

Figure 11
Cracking pattern in DB-WR-H1-1 (load in kN): (a) 30% of P_f ; (b) 50% of P_f ; (c) 70% of P_f ; (d) 90% of P_f ; (e) Failure.

Thumbnail

Figure 12
Cracking pattern in DB-WR-H1-2 (load in kN): (a) 30% of P_f ; (b) 50% of P_f ; (c) 70% of P_f ; (d) 90% of P_f ; (e) Failure.

Thumbnail

Figure 13
Cracking pattern in DB-NR-H2-1 (load in kN): (a) 30% of P_f ; (b) 50% of P_f ; (c) 70% of P_f ; (d) 90% of P_f ; (e) Failure.

Thumbnail

Figure 14
Cracking pattern in DB-NR-H2-2 (load in kN): (a) 30% of P_f ; (b) 50% of P_f ; (c) 70% of P_f ; (d) 90% of P_f ; (e) Failure.

Thumbnail

Figure 15
Cracking pattern in DB-WR-H2-1 (load in kN): (a) 30% of P_f ; (b) 50% of P_f ; (c) 70% of P_f ; (d) 90% of P_f ; (e) Failure.

Thumbnail

Figure 10
Cracking pattern in DB-NR-H1-2 (load in kN): (a) 85% of P_f ; (b) 95% of P_f ; (c) Failure.

Thumbnail

Figure 11
Cracking pattern in DB-WR-H1-1 (load in kN): (a) 30% of P_f ; (b) 50% of P_f ; (c) 70% of P_f ; (d) 90% of P_f ; (e) Failure.

Thumbnail

Figure 12
Cracking pattern in DB-WR-H1-2 (load in kN): (a) 30% of P_f ; (b) 50% of P_f ; (c) 70% of P_f ; (d) 90% of P_f ; (e) Failure.

Thumbnail

Figure 13
Cracking pattern in DB-NR-H2-1 (load in kN): (a) 30% of P_f ; (b) 50% of P_f ; (c) 70% of P_f ; (d) 90% of P_f ; (e) Failure.

Thumbnail

Figure 14
Cracking pattern in DB-NR-H2-2 (load in kN): (a) 30% of P_f ; (b) 50% of P_f ; (c) 70% of P_f ; (d) 90% of P_f ; (e) Failure.

Thumbnail

Figure 15
Cracking pattern in DB-WR-H2-1 (load in kN): (a) 30% of P_f ; (b) 50% of P_f ; (c) 70% of P_f ; (d) 90% of P_f ; (e) Failure.

Thumbnail

Figure 17
Load-strain curve

Thumbnail

Figure 20
Load-strain curve

Thumbnail

Figure 19
Load-strain curve

Thumbnail

Figure 18
Load-strain curve

Thumbnail

Figure 21
DB-H1 analysis results: (a) Principal compressive stress; (b) Principal tensile stress.

Thumbnail

Figure 22
DB-H2 analysis results: (a) Principal tensile stress; (b) Principal compressive stress.

Thumbnail

Figure 23
Comparison between the STM and experimental results

Thumbnail

Figure 24
Forces acting on each STM element

Thumbnail

Figure 25
Failure mode

Thumbnail

Figure 26
Comparison between the STM and experimental results.

Thumbnail

Figure 27
Forces acting on each STM element.

Thumbnail

Figure 28
Failure mode

Thumbnail

Figure 29
Comparison between the STM and experimental results

Thumbnail

Figure 30
Efforts acting on each element.

Thumbnail

Figure 31
Failure mode

Thumbnail

Figure 32
Comparison between the STM and experimental results

Thumbnail

Figure 33
Efforts acting on each element

Thumbnail

Figure 34
Failure mode

Thumbnail

Figure 23
Comparison between the STM and experimental results

Thumbnail

Figure 24
Forces acting on each STM element

Thumbnail

Figure 25
Failure mode

Thumbnail

Figure 26
Comparison between the STM and experimental results.

Thumbnail

Figure 27
Forces acting on each STM element.

Thumbnail

Figure 28
Failure mode

Thumbnail

Figure 29
Comparison between the STM and experimental results

Thumbnail

Figure 30
Efforts acting on each element.

Thumbnail

Figure 31
Failure mode

Thumbnail

Figure 32
Comparison between the STM and experimental results

Thumbnail

Figure 33
Efforts acting on each element

Thumbnail

Figure 34
Failure mode

Thumbnail

Table 1
Deep beam details

Thumbnail

Table 2
Mechanical properties of concrete

Thumbnail

Table 3
Mechanical properties of the reinforcement

Thumbnail

Table 4
Experimental results: cracking load, failure load and failure modes

Thumbnail

Table 5
Allowed ranges for the angle formed between the compressed diagonals and the longitudinal reinforcement in the STM.

Thumbnail

(1)

Deep Beams	L (mm)	h (mm)	b (mm)	L/h
DB-NR-H1-1	1000	700	140	1.43
DB-NR-H1-2
DB-WR-H1-1
DB-WR-H1-2
DB-NR-H2-1
DB-NR-H2-2
DB-WR-H2-1
DB-WR-H2-2

Age	f_c (MPa)	f_{c, average} (MPa)	E_c (GPa)	E_{c, average} (GPa)	f_ct,sp (MPa)	f_{ct,sp average} (MPa)
145th day	42.72	47.64	38.17	38.99	4.3	3.7
	47.74		38.17		4.3
	50.30		40.80		3.3
	47.49		40.80		3.3
	49.96		37.99		3.5

Ø (mm)	f_ys (MPa)	ε_ys (‰)	E_s (GPa)
6.3	594	2.88	206
8.0	614	3.04	202
10.0	551	2.87	192

Deep Beams	P_c (kN)	P_f (kN)	P_f,average (kN)	P_c/P_f (%)	Failure Modes
DB-NR-H1-1	159.00	193.68	200.67	82.09	Shear failure and anchorage failure
DB-NR-H1-2	186.00	207.66	200.67	89.57	Shear failure and anchorage failure
DB-WR-H1-1	160.00	474.90	407.99	33.69	Flexural failure
DB-WR-H1-2	199.00	341.07	407.99	58.34	Flexural failure
DB-NR-H2-1	133.00	210.12	233.74	63.30	Shear failure and anchorage failure
DB-NR-H2-2	133.00	257.37	233.74	51.67	Shear failure and anchorage failure
DB-WR-H2-1	150.00	305.61	307.07	49.08	Flexural-Shear failure
DB-WR-H2-2	117.00	308.52	307.07	37.92	Flexural-Shear failure

Normative/Author	Angle θ (°)
NBR 6118 [¹1 Associação Brasileira de Normas Técnicas, Design of concrete structures - procedure, NBR 6118, 2014.]	30° ≤ θ ≤ 63°
EUROCODE 2 [²⁸28 European Committee for Standardization, Eurocode 2: Design of Concrete Structures Part 1-1: General Rules and Rules for Buildings, EN 1992-1-1, 2004.]	21° ≤ θ ≤ 45°
ACI 318 [²⁷27 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI 318, 2019.]	25° ≤ θ ≤ 65°
Schlaich and Schäfer [³⁹39 [REMOVED IF= FIELD]39J. Schlaich and K. Schäfer, “Design and detailing of structural concrete using strut-and-tie models,” The Struct. Eng., vol. 32, pp. 133-125, 1991.]	45° ≤ θ ≤ 60°

[1] Corresponding author: Izabel Castro de Abreu Neta. E-mail: izabel.castroa@gmail.com

Brasil

Brasil

Resultados experimentais e análise de carga limite pelo Método de Bielas e Tirantes (MBT) de vigas-parede com entalhes e aberturas

Resumo