Analysis of shear strength of complementary mechanisms trends in reinforced concrete beams

Ribeiro, Igor José Santos; Pessoa, José Renato de Castro; Bittencourt, Túlio Nogueira

doi:10.1590/S1983-41952023000200008

Igor José Santos Ribeiro

Universidade de São Paulo – USP, Programa de Pós-graduação em Engenharia Civil, São Paulo, SP, Brasil

https://orcid.org/0000-0002-6622-6104

José Renato de Castro Pessoa

Universidade Estadual de Santa Cruz – UESC, Programa de Pós-graduação em Ciência, Inovação, e Modelagem de Materiais, Ilhéus, BA, Brasil

https://orcid.org/0000-0001-7641-4400

Túlio Nogueira Bittencourt

Universidade de São Paulo – USP, Programa de Pós-graduação em Engenharia Civil, São Paulo, SP, Brasil

https://orcid.org/0000-0001-6523-2687

Corresponding author: Igor José Santos Ribeiro. E-mail: ijoseribeiro@gmail.com

Conflict of interest: Nothing to declare.

Author contributions: JRCP: conceptualization, supervision, writing, methodology. TNB: Conceptualization, data curation, formal analysis, writing, methodology. IJSR: Conceptualization, data curation, formal analysis, writing, methodology

Editors: Edgar Bacarji, Guilherme Aris Parsekian.

Thumbnail

Figure 1
– (A) Shear span (a) to effective depth (d) to a point load (B) Kani’s valley

Thumbnail

Figure 2
- Dispersion points of analysis

Thumbnail

Figure 3
- Distribution of the data

Thumbnail

Figure 4
- S/R in relation to

f_{c}^{'}

to ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.] (yellow) and ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.] (blue)

Thumbnail

Figure 5
- S/R in relation to

a / d

to ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.] (yellow) and ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.] (blue)

Thumbnail

Figure 6
- S/R in relation to

ρ_{L}

to ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.] (yellow) and ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.] (blue)

Thumbnail

Figure 7
- S/R in relation to

d

to ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.] (yellow) and ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.] (blue)

Thumbnail

Figure 8
- S/R in relation to

f_{c}^{'}

to Frosch et al. [⁵5 R. J. Frosch et al., "A unified approach to design," Concr. Int., no. September, pp. 147–158, 2017.]

Thumbnail

Figure 9
- S/R in relation to

a / d

to Frosch et al. [⁵5 R. J. Frosch et al., "A unified approach to design," Concr. Int., no. September, pp. 147–158, 2017.]

Thumbnail

Figure 10
- S/R in relation to

ρ_{L}

to Frosch et al. [⁵5 R. J. Frosch et al., "A unified approach to design," Concr. Int., no. September, pp. 147–158, 2017.]

Thumbnail

Figure 11
- S/R in relation to

d

to Frosch et al. [⁵5 R. J. Frosch et al., "A unified approach to design," Concr. Int., no. September, pp. 147–158, 2017.]

Thumbnail

Figure 12
- S/R in relation to

f_{c}^{'}

to NBR 6118:2014

Thumbnail

Figure 13
- S/R in relation to

a / d

to NBR 6118:2014

Thumbnail

Figure 14
- S/R in relation to

ρ_{L}

to NBR 6118:2014

Thumbnail

Figure 15
- S/R in relation to

d

to NBR 6118:2014

Thumbnail

Figure 16
- Model Error (ME) to the proposed model.

Thumbnail

Figure 4
- S/R in relation to

f_{c}^{'}

to ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.] (yellow) and ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.] (blue)

Thumbnail

Figure 5
- S/R in relation to

a / d

to ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.] (yellow) and ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.] (blue)

Thumbnail

Figure 6
- S/R in relation to

ρ_{L}

to ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.] (yellow) and ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.] (blue)

Thumbnail

Figure 7
- S/R in relation to

d

to ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.] (yellow) and ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.] (blue)

Thumbnail

Figure 8
- S/R in relation to

f_{c}^{'}

to Frosch et al. [⁵5 R. J. Frosch et al., "A unified approach to design," Concr. Int., no. September, pp. 147–158, 2017.]

Thumbnail

Figure 9
- S/R in relation to

a / d

to Frosch et al. [⁵5 R. J. Frosch et al., "A unified approach to design," Concr. Int., no. September, pp. 147–158, 2017.]

Thumbnail

Figure 10
- S/R in relation to

ρ_{L}

to Frosch et al. [⁵5 R. J. Frosch et al., "A unified approach to design," Concr. Int., no. September, pp. 147–158, 2017.]

Thumbnail

Figure 11
- S/R in relation to

d

to Frosch et al. [⁵5 R. J. Frosch et al., "A unified approach to design," Concr. Int., no. September, pp. 147–158, 2017.]

Thumbnail

Figure 12
- S/R in relation to

f_{c}^{'}

to NBR 6118:2014

Thumbnail

Figure 13
- S/R in relation to

a / d

to NBR 6118:2014

Thumbnail

Figure 14
- S/R in relation to

ρ_{L}

to NBR 6118:2014

Thumbnail

Figure 15
- S/R in relation to

d

to NBR 6118:2014

Thumbnail

Figure 16
- Model Error (ME) to the proposed model.

Thumbnail

Table 1
- Expression of Reineck et al. [⁶6 K. H. Reineck et al., "ACI-DAfStb database of shear tests on slender reinforced concrete beams without stirrups," ACI Struct. J., vol. 110, no. 5, pp. 867–876, 2013.] applied to two specimens

Thumbnail

Table 2
- Upper Limits to 5 and 10%

Thumbnail

Table 3
- Upper Limits to 5 and 10%

Thumbnail

Table 4
- ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.] and ACI 318 [⁴4 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2019, 629 p.] results

Thumbnail

Table 5
– S/R x a/d results

Thumbnail

Table 6
- S/R x

ρ_{L}

results

Thumbnail

Table 7
- S/R x d results to ACI 318

Thumbnail

Table 8
- S/R x

f_{c}^{'}

to the Unified Approach

Thumbnail

Table 9
- S/R x a/d to the Unified Approach

Thumbnail

Table 10
– S/R x

ρ_{L}

to the Unified Approach

Thumbnail

Table 11
– S/R x

d

to the Unified Approach

Thumbnail

Table 12
– S/R x

f_{c k}

to NBR 6118: 2014

Thumbnail

Table 13
- S/R x a/d to NBR 6118: 2014

Thumbnail

Table 14
- S/R x

ρ_{L}

to NBR 6118: 2014

Thumbnail

Table 15
- S/R x d to NBR 6118 [⁹9 Associação Brasileira de Normas Técnicas, Design of Concrete Structures: Procedures, NBR 6118, 2014.]

Thumbnail

Parameter Design Formulation ABNT:NBR6118 (2014) ACI 318 (2014) ACI 318 (2019) Frosch et al. (2017) f c ' There is a decrease trend over the dataset, slightly more prominent A strong trend of decreasing in S/R mean as compressive strength increases Decreasing in S/R mean as compressive strength increases No trends are noted, and the approach is the more conservative a/d No trends concerning the mean, most of the results with S/R<1 is located next to inflection point of Kani’s valley No trends concerning the mean, most of the results with S/R<1 is located next to inflection point of Kani’s valley a slight decrease trend No strong trends are present ρ L Most of the values to which S/R<1 to light reinforced beams, with a strong increase trend Most of the values to which S/R<1 to light reinforced beams, with a strong increase trend Presents no notable trends regarding this parameter, No trends are present, and the results are dispersed in a more uniform manner d A strong decrease trends occurs, with excessively conservative design for shallow beams, decreasing until non conservative results to higher beam depth A strong decrease trends occurs, with excessively conservative design for shallow beams, decreasing until non conservative results to higher beam depth Significantly corrects the model error in shallow beams, leading to smaller S/R, and increasing its value as the beam depth increases This dispersion is like ACI 318:2019 but is more conservative, mainly to the smaller beam depths

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

Author	Specimen	$f_{c}^{'} (M P a)$	$f_{c k} (M P a)$
Drangsholt, G.; Thorenfeldt, E. (1992)	B11	51,60	$f_{c k} = 51,6 - 1,6 = 50,00$
Drangsholt, G.; Thorenfeldt, E. (1992)	B21	75,38	$f_{c k} = 75,38 - 1,6 = 73,78$

Model	Upper Limit (5%)	Upper Limit (5%)
ACI 318-14	2,42	2,09
ACI 318-19	2,17	1,87
Frosch et al. [⁵5 R. J. Frosch et al., "A unified approach to design," Concr. Int., no. September, pp. 147–158, 2017.]	2,37	1,97
NBR6118-14	2,61	2,20

Model	Upper Limit (5%)	Upper Limit (10%)
ACI 318-14	$U L = \bar{μ} + 2.33 C O V$	$U L = \bar{μ} + 1.50 C O V$
ACI 318-19	$U L = \bar{μ} + 2.70 C O V$	$U L = \bar{μ} + 1.50 C O V$
Frosch et al. [⁵5 R. J. Frosch et al., "A unified approach to design," Concr. Int., no. September, pp. 147–158, 2017.]	$U L = \bar{μ} + 3.14 C O V$	$U L = \bar{μ} + 1.92 C O V$
NBR6118-14	$U L = \bar{μ} + 2.51 C O V$	$U L = \bar{μ} + 1.51 C O V$

N	$f_{c}^{'}$ (MPa)	ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.]			ACI 318 [⁴4 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2019, 629 p.]
N	$f_{c}^{'}$ (MPa)	S/R<1 (%)	Mean	COV	S/R<1 (%)	Mean	COV
423	20-40	13.71	1.52	0.40	1.18	1.56	0.24
86	40-60	10.47	1.48	0.29	1.16	1.44	0.19
60	60-80	33.33	1.40	0.49	30,00	1.24	0.30
48	80-100	20.83	1.29	0.35	18.75	1.2	0.23

N	$a / d$ (-)	ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.]			ACI 318 [⁴4 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2019, 629 p.]
N	$a / d$ (-)	S/R<1 (%)	Mean	COV	S/R<1 (%)	Mean	COV
390	2.40 – 3.55	19.74	1.48	0.45	5.90	1.54	0.46
154	3.55 – 4.70	11.04	1.54	0.30	4.54	1.43	0.19
45	4.70 – 5.85	2.22	1.47	0.16	2.22	1.36	0.10
28	5.85 – 8.15	0.00	1.41	0.19	3.57	1.29	0.16

N	$ρ_{L}$ (%)	ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.]			ACI 318 [⁴4 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2019, 629 p.]
N	$ρ_{L}$ (%)	S/R<1 (%)	Mean	COV	S/R<1 (%)	Mean	COV
168	0-1.30	50.00	1.00	0.30	10.71	1.41	0.20
232	1.30 – 2.60	4.74	1.47	0.23	4.74	1.47	0.21
154	2.60 – 3.90	1.32	1.75	0.26	2.63	1.50	0.24
68	3.90 – 6.70	0.00	2.29	0.39	0.00	1.62	0.39

N	$d$ (mm)	ACI 318 [³3 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2014, 519 p.]			ACI 318 [⁴4 American Concrete Institute, Building Code Requirements for Structural Concrete, ACI Committee 318, 2019, 629 p.]
N	$d$ (mm)	S/R<1 (%)	Mean	COV	S/R<1 (%)	Mean	COV
225	0-250	1.78	1.86	0.35	2.22	1.58	0.28
298	250-500	10.40	1.40	0.27	4.36	1.42	0.19
37	500-750	48.65	1.09	0.34	18.92	1.39	0.25
33	750-1000	81.82	0.78	0.37	27.27	1.31	0.28
24	1000-2000	75.00	0.78	0.39	4.17	1.61	0.18

N	$f_{c}^{'}$ (MPa)	S/R<1 (%)	Mean	COV
423	20-40	0.44	1.61	0.28
86	40-60	0.00	1.59	0.20
60	60-80	10.00	1.50	0.35
48	80-100	0.00	1.52	0.21

N	a/d (-)	S/R<1 (%)	Mean	COV
392	2.40 – 3.55	0.26	1.84	0.25
154	3.55 – 4.70	0.00	1.51	0.16
47	4.70 – 5.85	0.00	1.43	0.12
25	5.85 – 8.15	0.00	1.45	0.20

N	$ρ_{L}$ (%)	S/R <1 (%)	Mean	COV
168	0-1.30	2.98	1.61	0.30
232	1.30 – 2.60	1.29	1.54	0.19
152	2.60 – 3.90	0.00	1.57	0.28
65	3.90 – 6.70	0.00	1.72	0.37

N	𝒅 (mm)	S/R <1 (%)	Mean	COV
225	0-250	0.00	1.70	0.25
298	250-500	0.34	1.48	0.20
37	500-750	10.81	1.49	0.32
33	750-1000	9.09	1.50	0.24
24	1000-2000	0.00	2.06	0.47

N	$f_{c k}$ (MPa)	S/R <1 (%)	Mean S/R	COV
423	20-40	11.35%	1.65	0.41
86	40-60	11.63%	1.48	0.29
60	60-80	31.67%	1.43	0.32
48	80-100	22.92%	1.29	0.37

N	𝒂/𝒅 (-)	S/R <1 (%)	Mean	COV
392	2.40 – 3.55	17.44	1.58	0.48
154	3.55 – 4.70	10.39	1.61	0.31
47	4.70 – 5.85	2.22	1.61	0.17
25	5.85 – 8.15	0.00	1.55	0.20

N	$ρ_{L}$ (%)	S/R <1 (%)	Mean	COV
168	0-1.30	44.05	1.05	0.32
232	1.30 – 2.60	5.17	1.54	0.25
152	2.60 – 3.90	1.32	1.87	0.27
65	3.90 – 6.70	0.00	2.42	0.42

N	$d$ (mm)	S/R <1 (%)	Mean	COV
225	0-250	2.22	1.96	0.38
298	250-500	9.40	1.49	0.28
37	500-750	37.84	1.14	0.38
33	750-1000	75.76	0.80	0.39
24	1000-2000	70.83	0.85	0.42

[1] Corresponding author: Igor José Santos Ribeiro. E-mail: ijoseribeiro@gmail.com

Brasil

Brasil

Analysis of shear strength of complementary mechanisms trends in reinforced concrete beams

Análise das tendências nos mecanismos complementares de resistência ao cisalhamento de vigas de concreto armado

abstract: