Influential parameters in the shear strength of RC beams without stirrups

Leme, Guilherme Frank; Liberati, Elyson Andrew Pozo; Marques, Marília Gonçalves; Trautwein, Leandro Mouta; Almeida, Luiz Carlos de

doi:10.1590/S1983-41952023000400006

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ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 16 (4) • 2023 • https://doi.org/10.1590/S1983-41952023000400006 copy

Influential parameters in the shear strength of RC beams without stirrups

Parâmetros que influenciam na resistência ao cisalhamento de vigas de concreto armado sem estribos

Authorship SCIMAGO INSTITUTIONS RANKINGS

abstract:

Experimental investigations have been commonly used to improve the existing knowledge about structural design, presenting accurate conclusions regarding structure behavior. However, considering the limitations of experimental studies, such as restricted amount of strain gauges, unexpected pathologies, difficulties to foresee the correct position of cracks, or simply saving in costs, the use of numerical analysis can present some innovative approaches to understand the process of failure in concrete elements, presenting easier results where experimental programs can hardly report. This study presents the numerical analysis of eight beams experimented by Sherwood [26], with two different sizes and variable aggregate sizes, seeking to understand the influence of coarse aggregate size in shear strength of beams without stirrups. The numerical approach was used to derive the influence of each internal shear mechanism and to identify the specific amount of dowel force, shear transfer by uncracked compression zone and aggregate interlock portion. The results showed that fair results can be obtained by 2D smeared crack approaches, enabling the identification of major aggregate interlock portion in beams with bigger coarse aggregate sizes. Comparing the size effect in beams allowed us to conclude that a higher contribution of aggregate interlock contribution can be obtained in large beams, with almost 64% of the total contribution, whereas smaller beams had only 43%. To evaluate the accuracy of the studied mechanisms, the results of Sherwood [26] were compared with the standards Model Code [23], CSA-A.23.3 [24], NBR 6118 [38], and ACI 318 [39]. Regarding the prediction of element rupture by concrete internal mechanisms, the normative instructions Model Code [23] and CSA A.23.3 [24] were the closest to the experimental results.

Keywords:
reinforced concrete; shear; numerical analysis; beams

Series	b_w [mm]	d [mm]	L [mm]	d_ag [mm]	f_c [MPa]	𝐴_𝑠₊ [mm²]
S-Series
S-10N1	122	280	1,620	9.5	41.9	285.2
S-10N2	122	280	1,620	9.5	41.9	285.2
S-20N1	122	280	1,620	19	39.2	285.2
S-20N2	122	280	1,620	19	38.1	285.2
S-40N1	122	280	1,620	38	29.1	285.2
S-40N2	122	280	1,620	38	29.1	285.2
S-50N1	122	280	1,620	51	43.5	285.2
S-50N2	122	280	1,620	51	43.5	285.2
L-Series
L-10N1	300	1,400	8,100	9.5	38.4	3,500.0
L-10N2	300	1,400	8,100	9.5	40.4	3,500.0
L-20N1	300	1,400	8,100	19	31.4	3,500.0
L-20N2	300	1,400	8,100	19	33.2	3,500.0
L-40N1	300	1,400	8,100	38	28.1	3,500.0
L-40N2	300	1,400	8,100	38	28.5	3,500.0
L-50N1	300	1,400	8,100	51	41.0	3,500.0
L-50N2	300	1,400	8,100	51	40.1	3,500.0

Bar type	Diameter [mm]	Area [mm²]	f_y [MPa]
#3	10	71.3	494
20M	20	300	484
30M	30	700	452

Specimen	S-10	S-20	S-40	S-50	L-10	L-20	L-40	L-50
d_ag [mm]	9.5	19	38	51	9.5	19	38	51
f_c [N/mm²]	41.9	38.1	29.1	43.5	38.4	31.4	28.1	40.1
f_ct [N/mm²]	2.5	2.4	2.1	2.3	2.35	1.96	1.94	2.20
E_c [N/mm²]	27,215	25,450	25,717	27,482	25,000	23,000	23,674	25,000
í Poisson	0.15	0.20	0.15	0.20	0.15	0.15	0.20	0.15
G_f [N mm/mm²]	0.049	0.065	0.090	0.078	0.040	0.045	0.069	0.072
G_c [N mm/mm²]	3.0	3.0	8.0	10.0	6.0	1.8	2.0	5.0
Smeared Crack Model	Fixed				Fixed
Tensile Softening	Exp.⁽¹⁾	Hordijk	Exp.⁽¹⁾	Exp.⁽¹⁾	Hordijk
Compression Diagram	Parabolic				Parabolic
Shear Retention Mode	Constant				Constant
â Shear Retention	0.01	0.03	0.008	0.013	0.033	0.033	0.043	0.033

d_max [mm]	G_F0 [N/mm]
8	0.025
16	0.030
32	0.058

Specimen	V_exp [kN]	Section	V_cz [kN]	%V_cz [%]	$\bar{V_{cz}}$ [kN]	V_dowel [kN]	V_agg [kN]	%V_agg [%]	% $\bar{V_{agg}}$ [%]
S-10	36.1	A	17.6	48.7	63.8	0.55	17.95	49.7	33.8
S-10	36.1	B	28.5	78.9	63.8	1.05	6.55	18.0	33.8
S-20	37.4	A	16.7	44.6	50.3	1.15	19.55	52.0	41.3
S-20	37.4	B	21.0	56.1	50.3	4.85	11.50	30.7	41.3
S-40	34.0	A	16.1	47.3	59.1	1.25	16.65	49.0	38.3
S-40	34.0	B	24.1	70.9	59.1	0.50	9.40	27.6	38.3
S-50	41.2	A	13.4	32.5	52.3	1.05	26.75	65.0	45.5
S-50	41.2	B	29.7	72.1	52.3	0.75	10.75	26.1	45.5
L-10	259.6	A	102.0	39.3	37.5	4.30	153.30	59.0	60.5
L-10	259.6	B	92.7	35.7	37.5	6.90	160.00	62.0	60.5
L-20	254.4	A	106.9	42.2	44.1	2.00	145.50	57.0	54.4
L-20	254.4	B	117.5	46.2	44.1	5.42	131.50	52.0	54.4
L-40	280.4	A	94.3	33.6	45.1	4.30	181.80	65.0	53.6
L-40	280.4	B	159.0	56.7	45.1	2.75	118.60	42.3	53.6
L-50	288.6	A	81.9	28.4	24.1	8.11	198.60	68.8	73.1
L-50	288.6	B	57.1	19.8	24.1	7.90	223.60	77.5	73.1

Specimen	V_exp [kN]	V_dowel,max [kN]	%V_dowel,max [%]
S-10	36.1	4.35	12.0
S-20	37.4	5.50	14.7
S-40	34.0	4.70	13.8
S-50	41.2	7.45	21.9
L-10	259.6	15.30	5.9
L-20	254.4	12.20	4.8
L-40	280.4	11.70	4.2
L-50	288.6	12.90	4.5

Specimen	V_exp [kN]	V_NBR [kN]	V_MC [kN]	V_CSA [kN]	V_ACI [kN]	V_exp/V_NBR	V_exp/V_MC	V_exp/V_CSA	V_exp/V_ACI
S-10N1	36.6	51.9	29.5	26.0	28.8	0.70	1.24	1.41	1.27
S-10N2	38.3	51.9	28.7	25.3	28.8	0.74	1.34	1.52	1.33
S-20N1	39.1	49.7	29.3	26.0	27.8	0.79	1.33	1.50	1.41
S-20N2	38.2	48.7	29.4	26.1	27.4	0.78	1.30	1.47	1.39
S-40N1	41.8	40.7	24.9	22.2	24.0	1.03	1.68	1.88	1.74
S-40N2	34.9	40.7	28.1	25.1	24.0	0.86	1.24	1.39	1.46
S-50N1	38.5	53.2	32.2	28.7	29.3	0.72	1.19	1.34	1.31
S-50N2	40.6	53.2	31.1	27.7	29.3	0.76	1.30	1.46	1.39
L-10N1	265.0	602.3	243.6	208.3	191.7	0.44	1.09	1.27	1.38
L-10N2	242.0	623.1	262.0	224.1	196.6	0.39	0.92	1.08	1.23
L-20N1	265.0	526.7	265.2	229.6	173.4	0.50	1.00	1.15	1.53
L-20N2	266.0	546.7	272.3	235.8	178.3	0.49	0.98	1.13	1.49
L-40N1	242.0	489.1	288.8	252.8	164.0	0.49	0.84	0.96	1.48
L-40N2	288.0	493.8	264.6	231.6	165.2	0.58	1.09	1.24	1.74
L-50N1	272.0	629.2	327.9	287.0	198.1	0.43	0.83	0.95	1.37
L-50N2	298.0	620.0	307.8	269.4	195.9	0.48	0.97	1.11	1.52
*Average*						0.64	1.15	1.30	1.44
CV (%)						29.0	19.6	18.6	10.1

IBRACON - Instituto Brasileiro do Concreto Instituto Brasileiro do Concreto (IBRACON), Av. Queiroz Filho, nº 1700 sala 407/408 Torre D, Villa Lobos Office Park, CEP 05319-000, São Paulo, SP - Brasil, Tel. (55 11) 3735-0202, Fax: (55 11) 3733-2190 - São Paulo - SP - Brazil
E-mail: arlene@ibracon.org.br

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[1] Corresponding author: Elyson Andrew Pozo Liberati. E-mail: eapliberati@uem.br