Experimental analysis of steel fiber reinforced concrete beams in shear

Nzambi, Aaron Kadima Lukanu Lwa; Oliveira, Dênio Ramam Carvalho de; Monteiro, Marcus Vinicius dos Santos; Silva, Luiz Felipe Albuquerque da

doi:10.1590/S1983-41952022000300001

Aaron Kadima Lukanu Lwa Nzambi

Universidade Federal do Pará – UFPA, Departamento de Engenharia Civil, Belém, PA, Brasil

http://orcid.org/0000-0002-6876-271X

Dênio Ramam Carvalho de Oliveira

Universidade Federal do Pará – UFPA, Departamento de Engenharia Civil, Belém, PA, Brasil

http://orcid.org/0000-0001-8254-4551

Marcus Vinicius dos Santos Monteiro

Universidade Federal do Pará – UFPA, Departamento de Engenharia Civil, Belém, PA, Brasil

http://orcid.org/0000-0001-7864-3944

Luiz Felipe Albuquerque da Silva

Universidade Federal do Pará – UFPA, Departamento de Engenharia Civil, Belém, PA, Brasil

http://orcid.org/0000-0001-5936-0762

Corresponding author: Aaron Kadima Lukanu Lwa Nzambi. E-mail: aaronkadima@email.com

Conflict of interest: Nothing to declare.

Author contributions: DRC: conceptualization, funding acquisition, supervision, writing; AKLL: conceptualization, data curation, formal analysis, methodology, writing; AKLL, MVS and LFA: data curation, formal analysis.

Editors: Ricardo Carrazedo, Guilherme Aris Parsekian.

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Figure 1
Flexure model of Model Code 10 [⁹9 International Federation for Structural Concrete, Model Code for Concrete Structures. Wilhelm Ernst & Sohn, 2013.].

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Figure 2
(a) Flat crimped steel fiber [¹1 A. K. L. L. Nzambi, D. R. C. Oliveira, A. M. Oliveira, and M. S. Picanço, "Pull-out tests of ribbed steel reinforcing bars embedded in concrete with steel fibres," Proc. Inst. Civ. Eng., Struct. Build., vol. 174, no. 3, pp. 181–189, 2021, http://dx.doi.org/10.1680/jstbu.17.00180.
http://dx.doi.org/10.1680/jstbu.17.00180... ] and (b) Reinforcing steel bars.

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Figure 3
Test schema.

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Figure 4
(a) Strain gauges model used for the concrete (EER_c), (b) Strain gauge on steel bar (EER_s) and (c) Detailing of beam sections.

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Figure 5
(a) Data acquisition equipment and (b) HUTM assembled test system.

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Figure 6
(a) Shear strength and (b) Shear stress.

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Figure 7
Failure pattern: (a) RC e (b) SFRC.

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Figure 8
Crack patterns.

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Figure 9
Concrete strains for RC and SFRC series.

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Figure 10
Strains in the longitudinal reinforcement for RC and SFRC series.

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Figure 11
Shear strength of the beams and strength gain.

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Figure 12
Influence of the flexural reinforcement rate on the failure mode: (a) Comparison with the V_flex/V_Exp relationship and (b) Comparison with the V_flex/V_MC10 relationship.

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Figure 13
Relationship between experimental and shear strength estimates: (a) With the series of beams without fiber and (b) With the series of beams with fiber.

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Figure 14
(a) Flexural response, (b) Softening Tensile response and (c) Rigid-plastic Tensile response

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Figure 7
Failure pattern: (a) RC e (b) SFRC.

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Figure 8
Crack patterns.

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Figure 9
Concrete strains for RC and SFRC series.

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Figure 10
Strains in the longitudinal reinforcement for RC and SFRC series.

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Figure 11
Shear strength of the beams and strength gain.

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Figure 12
Influence of the flexural reinforcement rate on the failure mode: (a) Comparison with the V_flex/V_Exp relationship and (b) Comparison with the V_flex/V_MC10 relationship.

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Figure 13
Relationship between experimental and shear strength estimates: (a) With the series of beams without fiber and (b) With the series of beams with fiber.

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Figure 14
(a) Flexural response, (b) Softening Tensile response and (c) Rigid-plastic Tensile response

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Table 1
Mixture Design.

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Table 2
Steel bars’ mechanical properties.

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Table 3
Characteristics of beams.

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Table 4
Loads and failure modes of the beams.

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Table 5
Failure mode evaluation.

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Table 6
Results estimated by the standards.

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Table 7
Classification according to Model Code 10 [⁹9 International Federation for Structural Concrete, Model Code for Concrete Structures. Wilhelm Ernst & Sohn, 2013.]

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Table 8
Residual stresses at SFRC flexure and tensile (Model Code 10) [⁹9 International Federation for Structural Concrete, Model Code for Concrete Structures. Wilhelm Ernst & Sohn, 2013.]

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Materials	Consumption (Kg/m³)
Materials	RC	SFRC
Portland CPII-Z32RS Cement	310.61
Coarse aggregate (pebble, d_max = 9.5 mm)	1078.53
Fine aggregate (fine sand)	781.49
Water	205
w/c	0.64
Steel Fiber	-	78.6
Superplasticizer Admixture	-	0.95

Location	∅ (mm)	$f_{y s}$ (MPa)	$ε_{y s}$ (‰)	$E_{s}$ (GPa)
Stirrups	4.2	651	5.20	203
Longitudinal reinforcement	6.3	540	4.40	225
	8.0	532	2.53	210
	10.0	521	2.45	212
	12.5	560	2.48	225

Series	Beams	$d$ (mm)	$a / d$	$ρ$ (%)	$C_{f}$ (%)	$f_{c}$ (MPa)
RC	VS-1	172	2	0.87	-	24.0
	VS-2			1.20		23.1
	VS-3			1.62		24.7
	VS-4			2.14		24.2
SFRC	VF-1			0.87	1	22.8
	VF-2			1.20		21.5
	VF-3			1.62		21.7
	VF-4			2.14		22.0

Series	Beam	ρ (%)	f_c (MPa)	V_Exp (kN)	V_cort,u (kN)	$v_{u}$ (MPa)	Failure mode
RC	VS-1	0.87	24.0	35.5	17.8	1.0	Shear
	VS-2	1.20	23.1	36.2	18.1	1.1
	VS-3	1.62	24.7	48.9	24.5	1.4
	VS-4	2.14	24.2	56.6	28.3	1.7
SFRC	VF-1	0.87	22.8	63.5	31.8	1.9
	VF-2	1.20	21.5	75.7	37.9	2.2
	VF-3	1.62	21.7	76.3	38.2	2.2
	VF-4	2.14	22.0	77.7	38.9	2.3

Type	Beam	$V_{f l e x}$ ₍_{Eq. 15}₎ (kN)	$V_{E x p}$ (kN)	$V_{M C 10}$ (kN)	$V_{f l e x} / V_{E x p}$	$V_{f l e x} / V_{M C 10}$	Failure mode
RC	VS-1	71.1	35.5	57.0	2.0	1.2	Shear
	VS-2	94.5	36.2	55.7	2.6	1.7
	VS-3	122.8	48.9	55.4	2.5	2.2
	VS-4	153.5	56.6	56.9	2.7	2.7
SFRC	VF-1	76.2	63.5	52.0	1.2	1.6
	VF-2	100.0	75.7	57.2	1.3	1.8
	VF-3	128.4	76.3	63.1	1.7	2.1
	VF-4	158.9	77.7	69.5	2.0	2.3

Beam	V_Exp (kN)		V_Exp / V_MC10	V_Exp / V_ACI	V_Exp / V_NBR	V_Exp / V_JSCE
		RC
VS-1	35.5		0.62	1.25	0.97	1.24
VS-2	36.2		0.65	1.31	1.00	1.16
VS-3	48.9		0.88	1.78	1.35	1.42
VS-4	56.6		0.99	2.01	1.57	1.48
Mean			0.79	1.59	1.22	1.32
Standard deviation			0.18	0.37	0.29	0.15
Coef. of variation (%)			23	23	24	0.11
		SFRC
VF-1	63.5		1.22	1.22	1.22	0.87
VF-2	75.7		1.33	1.33	1.33	1.01
VF-3	76.3		1.21	1.21	1.21	0.98
VF-4	77.7		1.12	1.12	1.12	0.95
Mean			1.22	1.22	1.22	0.95
Standard deviation			0.08	0.08	0.08	0.06
Coef. of variation (%)			7	7	7	6

Class	f_R3,k / f_R1,k	Behavior
a	0.5	Softening
b	0.7
c	0.9
d	1.1	Hardening
e	1.3	Hardening

Type	Beam	Class	Flexure		Tensile		Classification
Type	Beam	Class	f_R1,d (MPa)	f_R3,d (MPa)	f_Fts (MPa)	f_Ftuk,k (MPa)	f_R3,d / f_R1,d	Behavior
SFRC	VF-1	2.5c	2.5	2.3	1.1	0.65	0.92*	Softening
	VF-2
	VF-3
	VF-4

V_{M C 10, f} = \{0.18 \cdot k \cdot {[100 \cdot \frac{A_{s}}{b_{w} \cdot d} \cdot (1 + 7.5 \cdot \frac{f_{F t u k}}{f_{c t k}}) \cdot f_{c k}]}^{\frac{1}{3}} + 0.15 \cdot σ_{c p}\} \cdot b_{w} \cdot d

[1] Corresponding author: Aaron Kadima Lukanu Lwa Nzambi. E-mail: aaronkadima@email.com

Brasil

Brasil

Experimental analysis of steel fiber reinforced concrete beams in shear

Análise experimental de vigas de concreto armado com fibra de aço ao cisalhamento

Abstract