Reinforced concrete structures strengthened with CFRP (ACI x FIB) - Recommendations for bending design criteria

Orlando, Igor Del Gaudio; Bittencourt, Túlio Nogueira; Meneghetti, Leila Cristina

doi:10.1590/S1983-41952022000200004

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ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 15 (2) • 2022 • https://doi.org/10.1590/S1983-41952022000200004 copy

Reinforced concrete structures strengthened with CFRP (ACI x FIB) - Recommendations for bending design criteria

Reforço de estruturas de concreto armado com CFRP (ACI x FIB) - Recomendações para dimensionamento à flexão

Authorship Authorship SCIMAGO INSTITUTIONS RANKINGS

abstract:

This work deals with the evaluation of the design criteria and security check (Ultimate Limit State - ULS) of the American (ACI-440.2R, 2017) and European (FIB Model Code, 2010) standards of reinforced concrete structures strengthened with Carbon Fiber Reinforced Polymers (CFRP), by the technique of Externally Bonded Reinforcement (EBR). It is intended to evaluate if, for a given database of 64 experimental tests of beams and slabs, the obtained results respect the safety conditions according to the mentioned standards, to increase the efficiency of this reinforcement technique and to lead to the establishment of regulatory design criteria in Brazil. Results show a conservative match among experimental and theoretical values calculated according to the two guidelines and it is concluded that a future regulation in Brazil on this subject should be based on the FIB Model Code.

Keywords:
carbon fiber reinforced polymers (CFRP); bending strengthening; ACI-440 (2017); FIB Model Code (2010); regulation in Brazil

Author	Exp. Data	Type	Reinforced concrete element					CFRP System
			b	h	A_s	ρ_s	f^cil_cm	E_f1	ε_fk1	b_f1	t_f1	n_bf1	n_lf1	A_f1	ρ_f	ε_fu	Type
			(cm)	(cm)	(cm²)	(%)	(MPa)	(GPa)	(‰)	(mm)	(mm)	n_bf1	n_lf1	(cm²)	(%)	(‰)	Rupt.
Dias [³⁷37 S. Dias, “Verificação experimental do reforço com CFRP de estruturas de betão à flexão,” M.S. thesis, Fac. Eng., Univ. Porto (FEUP), Porto, 2001.]	LA3R	S.	44.0	7.6	0.85	0.31%	63.3	230	15	140	0.11	1	2	0.311	0.09%	11.1	RC
	LB1R	S.	44.0	8.1	0.85	0.28%	63.3	230	15	140	0.11	1	2	0.311	0.09%	12.0	RC
	LA4S	L.	44.0	8.0	0.85	0.29%	63.3	160	20	32	1.20	1	1	0.384	0.11%	9.7	RP
	LB2S	L.	44.0	8.5	0.85	0.27%	63.3	160	20	32	1.20	1	1	0.384	0.10%	9.2	RP
	LD3BL	L.	44.0	8.5	0.85	0.27%	49.7	150	14	32	1.40	1	1	0.448	0.12%	9.6	RP
	LD4BL	L.	44.0	8.1	0.85	0.28%	49.7	150	14	32	1.40	1	1	0.448	0.13%	10.4	RP
	LE3I	L.	44.0	8.2	0.85	0.28%	49.7	160	15	32	1.40	1	1	0.448	0.12%	8.6	RP
	LE4I	L.	44.0	7.8	0.85	0.30%	49.7	160	15	32	1.40	1	1	0.448	0.13%	10.2	RP
Juvandes [²⁴24 L. F. P. Juvandes, “Reforço e reabilitação de estruturas de betão usando materiais compósitos de CFRP,” Ph.D. dissertation, Fac. Eng., Univ. Porto, 1999.]	LC3R	S.	44.0	8.1	0.85	0.28%	63.3	230	15	140	0.11	1	2	0.311	0.09%	10.9	RC
	LC4R	S.	44.0	7.7	0.85	0.30%	63.3	230	15	140	0.11	1	2	0.311	0.09%	10.3	RC
	LC1S	L.	44.0	8.1	0.85	0.28%	63.3	160	20	32	1.20	1	1	0.384	0.11%	10.3	RP
	LC2S	L.	44.0	8.4	0.85	0.27%	63.3	160	20	32	1.20	1	1	0.384	0.10%	11.8	RP

Author	Exp. Data	Type	Reinforced concrete element					CFRP System
			b	h	A_s	ρ_s	f^cil_cm	E_f1	ε_fk1	b_f1	t_f1	n_bf1	n_lf1	A_f1	ρ_f	ε_fu	Type
			(cm)	(cm)	(cm²)	(%)	(MPa)	(GPa)	(‰)	(mm)	(mm)	n_bf1	n_lf1	(cm²)	(%)	(‰)	Rupt.
Dias [³⁷37 S. Dias, “Verificação experimental do reforço com CFRP de estruturas de betão à flexão,” M.S. thesis, Fac. Eng., Univ. Porto (FEUP), Porto, 2001.]	V2	S	12.0	18.0	1.01	0.52%	41.0	240	15	70	0.11	1	2	0.155	0.07%	8.1	RP
	V3	S	12.0	18.0	1.01	0.52%	41.0	240	15	70	0.11	1	2	0.155	0.07%	8.1	RC
	V4	L	12.0	18.0	1.01	0.52%	41.0	200	11	20	1.40	1	1	0.280	0.13%	6.9	RP
	V6	L	12.0	18.0	1.01	0.52%	41.0	200	11	20	1.40	1	1	0.280	0.13%	7.2	RP
Pinto [⁴¹41 C. Pinto, “Reforço à flexão de vigas de concreto armado com fibras de carbono,” M.S. thesis, Univ. Fed. Rio de Janeiro, Rio de Janeiro, 2000.]	V1	L	15.0	45.0	6.03	0.98%	34.8	165	17	50	1.20	2	1	1.200	0.18%	5.2	RP
	V3	L	15.0	45.0	6.03	0.98%	38.3	165	17	50	1.20	3	1	1.800	0.27%	5.4	RP
	V5	L	15.0	45.0	6.03	0.97%	34.7	165	17	50	1.20	3	1	1.800	0.44%	4.6	RC
Beber [³⁸38 A. Beber, “Avaliação do Desempenho de Vigas de Concreto Armado Reforçadas com Lâminas de Fibra de Carbono,” Ph.D. dissertation, Univ. Fed. Rio Grande do Sul (UFRGS), Porto Alegre, 1999.]	VR3	L	12.0	25.0	1.57	0.57%	33.6	230	15	100	0.11	1	1	0.111	0.04%	5.6	RC
	VR4	L	12.0	25.0	1.57	0.57%	33.6	230	15	100	0.11	1	1	0.111	0.04%	7.1	RC
	VR5	L	12.0	25.0	1.57	0.57%	33.6	230	15	100	0.11	1	4	0.444	0.15%	7.1	RP
	VR6	L	12.0	25.0	1.57	0.57%	33.6	230	15	100	0.11	1	4	0.444	0.15%	7.5	RP
	VR7	L	12.0	25.0	1.57	0.57%	33.6	230	15	100	0.11	1	7	0.777	0.26%	5.2	RP
	VR8	L	12.0	25.0	1.57	0.57%	33.6	230	15	100	0.11	1	7	0.777	0.26%	5.6	RP
	VR9	L	12.0	25.0	1.57	0.57%	33.6	230	15	100	0.11	1	10	1.110	0.37%	4.8	RP
	VR10	L	12.0	25.0	1.57	0.57%	33.6	230	15	100	0.11	1	10	1.110	0.37%	4.7	RP
Travassos [⁴²42 N. Travassos, “Caracterização do comportamento da ligação CFRP-Betão,” M.S. thesis, Inst. Superior Técnico (IST), Lisboa, 2005.]	A12	L	20.0	40.0	4.02	0.59%	38.5	242	16	200	0.11	1	3	0.666	0.08%	8.0	RP
	A14	L	20.0	40.0	4.02	0.59%	38.5	242	16	200	0.11	1	1	0.222	0.03%	6.2	RC
	A32	L	20.0	40.0	4.02	0.59%	38.5	242	16	200	0.11	1	3	0.666	0.08%	7.2	RP
	A33	L	20.0	40.0	4.02	0.59%	38.5	242	16	200	0.11	1	1	0.222	0.03%	3.2	RC
	A11	L	20.0	40.0	4.02	0.59%	34.4	242	16	200	0.11	1	1	0.222	0.03%	6.7	RC
	A21	L	20.0	40.0	9.42	1.39%	34.4	242	16	200	0.11	1	1	0.222	0.03%	9.2	RC
	A31	L	20.0	40.0	4.02	0.59%	34.4	242	16	200	0.11	1	3	0.666	0.08%	10.6	RP
	A34	L	20.0	40.0	4.02	0.59%	34.4	242	16	200	0.11	1	1	0.222	0.03%	8.4	RC
Matthys [⁴⁰40 S. Matthys, “Structural behaviour and design of concrete members strengthened with externally bonded FRP reinforcement,” Ph.D. dissertation, Ghent Univ., Ghent, 2000.]	BF2	L	20.0	45.0	8.04	0.96%	36.5	159	19	100	1.20	1	1	1.200	0.13%	6.7	RP
	BF3	L	20.0	45.0	8.04	0.96%	34.9	159	19	100	1.20	1	1	1.200	0.13%	7.2	RP
	BF4	L	20.0	45.0	8.04	0.96%	30.8	159	19	100	1.20	1	1	1.200	0.13%	6.8	RP
	BF5	L	20.0	45.0	8.04	0.96%	37.4	159	19	100	1.20	1	1	1.200	0.13%	5.7	RP
	BF6	L	20.0	45.0	8.04	0.96%	35.9	159	19	100	1.20	1	1	1.200	0.13%	7.1	RP
	BF8	L	20.0	45.0	4.02	0.48%	39.4	159	19	100	1.20	1	1	1.200	0.13%	5.8	RC
	BF9	S	20.0	45.0	4.02	0.48%	33.7	233	13	100	0.11	1	2	0.222	0.02%	10.0	RP
Brosens [³⁹39 K. Brosens, “Anchorage of externally bonded steel plates and CFRP laminates for the strengthening of concrete elements,” Ph.D. dissertation, Katholieke Univ. Leuven, Leuven, Bélgica, 2001.]	A1	S	12.5	22.5	1.01	0.41%	41.0	235	15	75	0.17	1	2	0.251	0.09%	-	RP
	B1	S	12.5	22.5	1.51	0.62%	46.0	235	15	75	0.17	1	2	0.251	0.09%	-	RP
	C1	S	12.5	22.5	1.51	0.62%	43.0	235	15	75	0.17	1	2	0.251	0.09%	-	RP
	C2	S	12.5	22.5	1.51	0.62%	43.0	235	15	75	0.17	1	2	0.251	0.09%	-	RP
	D1	S	12.5	22.5	1.51	0.62%	38.0	235	15	75	0.17	1	2	0.251	0.09%	-	RP
	E1	S	12.5	22.5	1.51	0.62%	33.0	235	15	75	0.17	1	2	0.251	0.09%	-	RP
	F1	S	12.5	22.5	1.29	0.52%	43.0	235	15	75	0.17	1	2	0.251	0.09%	-	RP
	G1	S	12.5	22.5	2.07	0.85%	43.0	235	15	75	0.17	1	2	0.251	0.09%	-	RP
Gamino et al. [²¹21 A. L. Gamino, T. N. Bittencourt, and J. L. A. O. Sousa, "Estruturas de concreto reforçadas com PRFC. Parte I: análise dos modelos de flexão," Rev. IBRACON, vol. 2, no. 4, pp. 326–355, 2009, http://dx.doi.org/10.1590/S1983-41952009000400003. http://dx.doi.org/10.1590/S1983-41952009... ]	VR01	L	7.5	15.0	0.62	0.62%	45.0	230	15	75	0.13	1	1	0.098	0.09%	13.3	RC
	VR02	L	7.5	15.0	0.62	0.62%	45.0	230	15	75	0.13	1	1	0.098	0.09%	-	RC
	VR03	L	7.5	15.0	0.62	0.62%	45.0	230	15	75	0.13	1	1	0.098	0.09%	11.8	RC
	VR04	L	7.5	15.0	0.62	0.62%	45.0	230	15	75	0.13	1	1	0.098	0.09%	12.6	RC
	VR05	L	7.5	15.0	0.62	0.62%	45.0	230	15	75	0.13	1	1	0.098	0.09%	11.4	RC
	VR06	L	7.5	15.0	0.62	0.62%	45.0	230	15	75	0.13	1	1	0.098	0.09%	-	RP
	VR07	L	7.5	15.0	0.62	0.62%	45.0	230	15	75	0.13	1	1	0.098	0.09%	-	RP
	VR08	L	7.5	15.0	0.62	0.62%	45.0	230	15	75	0.13	1	1	0.098	0.09%	-	RP
	VR09	S	7.5	15.0	0.62	0.62%	45.0	235	15	75	0.11	1	1	0.083	0.07%	5.3	RC
	VR10	S	7.5	15.0	0.62	0.62%	45.0	235	15	75	0.11	1	1	0.083	0.07%	6.4	RC
	VR11	S	7.5	15.0	0.62	0.62%	45.0	235	15	75	0.11	1	2	0.165	0.15%	6.6	RC
	VR12	S	7.5	15.0	0.62	0.62%	45.0	235	15	75	0.11	1	1	0.083	0.07%	4.3	RC
	VR13	S	7.5	15.0	0.62	0.62%	45.0	235	15	75	0.11	1	1	0.083	0.07%	4.4	RC
	VR14	S	7.5	15.0	0.62	0.62%	45.0	235	15	75	0.11	1	1	0.083	0.07%	3.9	RC

Parameters established for the analysis criteria
	Partial safety factor
	C.1	C.2	C.5	C.6
Design equations.	(ACI)	(FIB)	(ACI)	(FIB)
Material properties	(ACI)	(FIB)	(ACI)	(FIB)
Ultimate compressive strain of concrete; (ε_cu)	3‰	3.5‰	3‰	3.5‰
Limit of tensile strain in steel (ε_s,lim)	-	-	-	-
Strength reduction factor (ф)	1	1	(Δε_s)	Verification
FRP Strength reduction factor (ѱ_f)	1	1	0.85	-
Partial safety factor for steel (γ_s)	1	1	1.10	1.15
Environmental reduction factor (C_E)	1	1	0.85	0.74

$(M_{t h e o r e t .}$ / $M_{e x p} .)$ of 64 experimental data
										ACI	FIB
										(C.1)	(C.2)
						ACI	FIB	Slab (Laminates)	Mean	0.75	0.82
						(C.1)	(C.2)		SD	0.05	0.05
				Total Slab	Mean	0.88	0.92		CV(%)	6.28	5.71
		ACI	FIB		SD	0.21	0.17	Slab (Sheet)	Mean	1.15	1.14
		(C.1)	(C.2)		CV(%)	23.31	18.19		SD	0.08	0.08
Total	Mean	0.92	0.95						CV(%)	7.23	7.23
	SD	0.15	0.15	Total Beam	Mean	0.93	0.96	Beam (Laminates)	Mean	0.97	0.98
	CV(%)	16.73	16.04		SD	0.15	0.15		SD	0.15	0.13
					CV(%)	16.02	15.71		CV(%)	15.11	13.73
								Beam (Sheet)	Mean	0.85	0.86
									SD	0.13	0.16
									CV(%)	14.88	18.20
( $ε_{t h e o r e t .}$ / $ε_{e x p} .$ ₎ of 52 experimental data ^* * 12 of 64 experimental strain data collected (εexp) are unknown.
										ACI	FIB
										(C.1)	(C.2)
						ACI	FIB	Slab (Laminates)	Mean	0.69	0.81
						(C.1)	(C.2)		SD	0.08	0.08
				Total Slab	Mean	0.89	0.97		CV(%)	11.39	10.17
		ACI	FIB		SD	0.31	0.24	Slab (Sheet)	Mean	1.30	1.27
		(C.1)	(C.2)		CV(%)	34.65	24.89		SD	0.08	0.08
Total	Mean	1.32	1.38						CV(%)	6.27	6.27
	SD	0.79	0.84	Total Beam	Mean	1.44	1.50	Beam (Laminates)	Mean	1.29	1.28
	CV(%)	60.19	61.08		SD	0.85	0.92		SD	0.83	0.78
					CV(%)	58.82	61.09		CV(%)	64.21	60.62
								Beam (Sheet)	Mean	1.99	2.27
									SD	0.73	1.00
									CV(%)	36.53	43.99

Global safety factor (C.1/C.5) - ACI
						FR	Mean	1.35
			Slab	Mean	1.31		SD	0.06
				SD	0.07		CV(%)	4.19
Total	Mean	1.28		CV(%)	5.66	FD	Mean	1.27
	SD	0.05					SD	0.04
	CV(%)	3.97	Beam	Mean	1.27		CV(%)	3.20
				SD	0.04	CC	Mean	1.25
				CV(%)	3.12		SD	0.02
							CV(%)	1.24
Global safety factor (C.2/C.6) - FIB
						FR	Mean	1.35
			Slab	Mean	1.26		SD	0.03
				SD	0.09		CV(%)	2.40
Total	Mean	1.32		CV(%)	7.25	FD	Mean	1.24
	SD	0.08					SD	0.06
	CV(%)	5.88	Beam	Mean	1.33		CV(%)	5.01
				SD	0.07	CC	Mean	1.37
				CV(%)	5.40		SD	0.03
							CV(%)	2.47

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[1] Corresponding author: Igor Del Gaudio Orlando. E-mail: igordgorlando@gmail.com