Analysis of the efficiency of strengthening design models for reinforced concrete columns

This paper develops a comparative analysis of the main design models used for predicting the strengthening of reinforced concrete columns subjected to uniaxial compression. The study evaluated four strengthening design models with concrete jackets and eleven strengthening design models with wrapping in Carbon Fiber-Reinforced Polymer (CFRP). All models consider the effect of confinement provided by the transverse steel reinforcement and the CFRP sheet wrapping on the gain in resistance of the column. For the validation, a database was formulated containing 135 experimental results of columns tested by several researches, which was used to analyze all design models and identify which was best for expressing the behavior of the strengthened column. At the end of the study, one confinement design model with transverse reinforcement and eleven design models with confinement provided by CFRP sheet wrapping and transverse steel reinforcement which showed the best resistance predictions were selected.

Keywords:
strengthening; confinement; carbon fibers; concrete jacketing; design models

Authorship

P. C. RODRIGUES

Universidade Federal de Goiás, Goiânia, GO, Brasil. patriciarodgs@gmail.com dlaraujo@ufg.brUniversidade Federal de GoiásBrazilGoiânia, GO, BrazilUniversidade Federal de Goiás, Goiânia, GO, Brasil. patriciarodgs@gmail.com dlaraujo@ufg.br

D. L. ARAÚJO

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables

Figures (11)
Tables (13)

Reference	Confinement type	f_cc
Samaan et al. [10]	GFRP	$f_{c} + 6.0 f_{l, f}^{0.7}$
Miyauchi et al. [11]	CFRP	$f_{c} [1 + 3.5 \frac{f_{l, f}}{f_{c}}]$
Kono et al. [12]	CFRP	$f_{c} (1 + 0.0572 f_{l, f})$
Toutanji [13]	CFRP GFRP	$f_{c} [1 + 3.5 {(\frac{f_{l, f}}{f_{c}})}^{0.85}]$
Saafi et al. [14]	CFRP GFRP	$f_{c} [1 + 2.2 {(\frac{f_{l, f}}{f_{c}})}^{0.84}]$
Spoelstra and Monti [15]	CFRP GFRP	$f_{c} [0.2 + 3 {(\frac{f_{l, f}}{f_{c}})}^{0.5}]$
Fardis and Khalili [16]	GFRP	$f_{c} (1 + 2.05 \frac{f_{l, f}}{f_{c}})$
Karbhari and Eckel [17]	CFRP GFRP AFRP	$f_{c} [1 + 2.1 {(\frac{f_{l, f}}{f_{c}})}^{0.87}]$
Mirmiran and Shahawy [18]	GFRP	$f_{c} + 4.269 f_{l, f}^{0.587}$
Shehata, Carneiro, and Shehata [19]	CFRP	$f_{c} (1 + β \frac{f_{l, f}}{f_{c}}) *$

Model	F_u,exp (kN)	Cusson and Paultre [2]		Saatcioglu and Razvi [3]		Frangou et al. [4]		fib Model Code 2010 [5]
Model	F_u,exp (kN)	F_u,theor (kN)	Δ	F_u,theor (kN)	Δ	F_u,theor (kN)	Δ	F_u,theor (kN)	Δ
S1C1S	1540	1356	0.88	1394	0.91	1324	0.86	1340	0.87
S1C2S	1749	1276	0.73	1295	0.74	1320	0.75	1259	0.72
S2C1S	1850	1841	0.99	1876	1.01	1813	0.98	1823	0.99
S1C2S	1840	1749	0.95	1765	0.96	1780	0.97	1727	0.94
Mean	-	-	0.89	-	0.90	-	0.89	-	0.88
CV*	-	-	0.13	-	0.13	-	0.12	-	0.13

Reference	Column	Dimensions				FRP				Experimental conditions
Reference	Column	D (mm)	H (mm)	λ	Fiber type	t_f (mm)	ξ_f (‰)	E_f (MPa)	f_f (MPa)	n	f_c (MPa)	f_l (MPa)	f_cc,exp (MPa)
Carrazedo [6]	C1	190	570	12	CFRP	0.130	11.92	218950	2610	1	26.16	3.57	38.81
Carrazedo [6]	C2	190	570	12	CFRP	0.130	10.89	218950	2384	2	26.16	6.53	53.08
Shehata, Carneiro, and Shehata [19]	C1-25a	150	300	8	CFRP	0.165	15.00	235000	3525	1	25.60	7.76	43.90
	C2-30a	150	300	8	CFRP	0.165	15.00	235000	3525	1	29.80	7.76	57.00
	C1-25b	150	300	8	CFRP	0.165	15.00	235000	3525	2	25.60	15.51	59.60
	C2-30b	150	300	8	CFRP	0.165	15.00	235000	3525	2	29.80	15.51	72.10
Samaan et al. [10]	DA11	153	305	8	GFRP	0.240	-	-	579.2	6	30.86	10.94	53.66
	DA13	153	305	8	GFRP	0.240	-	-	579.2	6	30.86	10.94	56.50
	DB11	153	305	8	GFRP	0.240	-	-	579.2	6	29.64	10.94	67.12
	DB12	153	305	8	GFRP	0.240	-	-	579.2	6	29.64	10.94	55.29
	DB13	153	305	8	GFRP	0.240	-	-	579.2	6	29.64	10.94	60.23
	DC11	153	305	8	GFRP	0.240	-	-	579.2	6	31.97	10.94	59.06
	DC12	153	305	8	GFRP	0.240	-	-	579.2	6	31.97	10.94	60.79
	DA21	153	305	8	GFRP	0.220	-	-	579.2	10	30.86	16.71	72.92
	DA22	153	305	8	GFRP	0.220	-	-	579.2	10	30.86	16.71	65.67
	DA23	153	305	8	GFRP	0.220	-	-	579.2	10	30.86	16.71	77.99
	DB21	153	305	8	GFRP	0.220	-	-	579.2	10	29.64	16.71	74.56
	DB22	153	305	8	GFRP	0.220	-	-	579.2	10	29.64	16.71	93.02
	DB23	153	305	8	GFRP	0.220	-	-	579.2	10	29.64	16.71	71.77
	DC21	153	305	8	GFRP	0.220	-	-	579.2	10	31.97	16.71	77.35
	DC22	153	305	8	GFRP	0.220	-	-	579.2	10	31.97	16.71	77.08
	DA31	153	305	8	GFRP	0.212	-	-	579.2	14	30.86	22.56	85.72
	DA33	153	305	8	GFRP	0.212	-	-	579.2	14	30.86	22.56	86.76
	DB31	153	305	8	GFRP	0.212	-	-	579.2	14	29.64	22.56	86.22
	DB32	153	305	8	GFRP	0.212	-	-	579.2	14	29.64	22.56	114.66
	DB33	153	305	8	GFRP	0.212	-	-	579.2	14	29.64	22.56	87.44
	DC31	153	305	8	GFRP	0.212	-	-	579.2	14	31.97	22.56	86.11
	DC32	153	305	8	GFRP	0.212	-	-	579.2	14	31.97	22.56	83.99
Eid, Roy, and Paultre [20]	N1	152	300	8	CFRP	0.381	13.40	78000	1045	1	32.10	5.24	39.71
	N2	152	300	8	CFRP	0.381	13.40	78000	1045	2	32.10	10.48	57.58
	N3	152	300	8	CFRP	0.381	13.40	78000	1045	3	33.60	15.72	74.24
	M1	152	300	8	CFRP	0.381	13.40	78000	1045	1	48.00	5.24	59.80
	M2	152	300	8	CFRP	0.381	13.40	78000	1045	2	48.00	10.48	80.04
	M3	152	300	8	CFRP	0.381	13.40	78000	1045	3	48.00	15.72	99.84
Wang et al. [21]	C1H0L1M	305	915	12	CFRP	0.167	17.79	244000	4340	1	24.50	4.75	35.00
	C1H0L2M	305	915	12	CFRP	0.167	17.79	244000	4340	2	24.50	9.51	55.30
	C2H0L1M	204	612	12	CFRP	0.167	17.79	244000	4340	1	24.50	7.11	46.10
	C2H0L2M	204	612	12	CFRP	0.167	17.79	244000	4340	2	24.50	14.21	65.20
Lee et al. [22]	S0F1	150	300	8	CFRP	0.110	18.04	250000	4510	1	36.20	6.61	41.70
	S0F2	150	300	8	CFRP	0.110	18.04	250000	4510	2	36.20	13.23	57.80
	S0F3	150	300	8	CFRP	0.110	18.04	250000	4510	3	36.20	19.84	69.10
	S0F4	150	300	8	CFRP	0.110	18.04	250000	4510	4	36.20	26.46	85.40
	S0F5	150	300	8	CFRP	0.110	18.04	250000	4510	5	36.20	33.07	104.30

Reference	f_cc,theor/f_cc,exp
Reference	Fardis and Khalili [16]	Karbhari and Eckel [17]	Mirmiran and Shahawy [18]	Miyauchi et al. [11]	Samaan et al. [10]	Saafi et al. [14]	Toutanji [13]	Spoelstra and Monti [15]	Kono et al. [12]	Shehata, Carneiro, and Shehata [19]
Mean	0.90	0.96	0.78	1.20	1.04	0.99	1.29	1.01	0.85	0.89
CV	0.12	0.12	0.17	0.12	0.12	0.12	0.11	0.11	0.15	0.12

Reference	T
Fardis and Khalili [16]	5.57413
Karbahari and Eckel [17]	2.83641
Mirmiran and Shahawy [18]	8.84600
Miyauchi et al. [11]	-7.66059
Samaan et al. [10]	-0.83592
Saafi et al. [14]	1.08314
Toutanji [13]	-11.17020
Spoelstra and Monti [15]	-0.10101
Kono et al. [12]	6.71226
Shehata, Carneiro and Shehata [19]	6.08063

Reference	F_u,theor/F_u,exp
Reference	Cusson and Paultre [2]	Saatcioglu and Razvi [3]	Frangou et al. [4]	fib Model Code 2010 [5]
Mean	0.90	1.02	0.88	0.97
CV	0.06	0.08	0.06	0.08

Reference	t
Cusson and Paultre [2]	5.40745
Saatcioglu and Razvi [3]	-0.02044
Frangou et al. [4]	5.91667
fib Model Code 2010 [5]	1.99189

Reference	Model	Dimensions of column and concrete strength				FRP				Longitudinal reinforcement				Transverse reinforcement
Reference	Model	D (mm)	H (mm)	c (cm)	f_c (MPa)	Fiber type	t_f (mm)	ξ_f (‰)	E_f (MPa)	n	φ_l (cm)	nº	f_y,l (MPa)	Type	φ_t (cm)	s (mm)	f_y,t (MPa)
Carrazedo [6]	C1S50	190	570	1.5	26.16	CFRP	0.130	11.00	218950	1	0.8	6	554.8	Spirals	0.50	50	756
	C2S50	190	570	1.5	26.16	CFRP	0.130	8.78	218950	2	0.8	6	554.8	Spirals	0.50	50	756
	C1S25	190	570	1.5	28.86	CFRP	0.130	10.63	218950	1	0.8	6	554.8	Spirals	0.50	25	756
	C2S25	190	570	1.5	28.86	CFRP	0.130	10.65	218950	2	0.8	6	554.8	Spirals	0.50	25	756
Eid, Roy, and Paultre [20]	A5NP2C	303	1200	2.5	29.40	CFRP	0.381	13.40	78000	2	1.6	6	423	Stirrups	0.95	150	602
	A3NP2C	303	1200	2.5	31.70	CFRP	0.381	13.40	78000	2	1.6	6	550	Stirrups	0.95	70	602
	A1NP2C	303	1200	2.5	31.70	CFRP	0.381	13.40	78000	2	1.6	6	486.5	Stirrups	0.95	45	602
	C4NP2C	303	1200	2.5	31.70	CFRP	0.381	13.40	78000	2	1.6	6	423	Stirrups	1.13	100	456
	C4N1P2C	303	1200	2.5	36.00	CFRP	0.381	13.40	78000	2	1.6	6	423	Spirals	1.13	100	456
	C4NP4C	303	1200	2.5	31.70	CFRP	0.381	13.40	78000	4	1.6	6	423	Spirals	1.13	100	456
	B4NP2C	303	1200	2.5	31.70	CFRP	0.381	13.40	78000	2	1.6	6	550	Stirrups	1.13	100	456
	C4MP2C	303	1200	2.5	50.80	CFRP	0.381	13.40	78000	2	1.6	6	423	Spirals	1.13	100	456
	C2NP2C	303	1200	2.5	31.70	CFRP	0.381	13.40	78000	2	1.6	6	423	Spirals	1.13	65	456
	C2N1P2C	303	1200	2.5	36.00	CFRP	0.381	13.40	78000	2	1.6	6	423	Spirals	1.13	65	456
	C2N1P4C	303	1200	2.5	36.00	CFRP	0.381	13.40	78000	4	1.6	6	423	Spirals	1.13	65	456
	C2MP2C	303	1200	2.5	50.80	CFRP	0.381	13.40	78000	2	1.6	6	423	Spirals	1.13	65	456
	C2MP4C	303	1200	2.5	50.80	CFRP	0.381	13.40	78000	4	1.6	6	423	Spirals	1.13	65	456
Huang et al. [23]	P1S1	150	300	0	30.04	GFRP	0.436	16.00	60800	1	-	-	-	Spirals	0.80	25	356
	P2S1	150	300	0	30.04	GFRP	0.436	16.00	60800	2	-	-	-	Spirals	0.80	25	356
	P3S1	150	300	0	30.04	GFRP	0.436	16.00	60800	3	-	-	-	Spirals	0.80	25	356
	P1S2	150	300	0	30.04	GFRP	0.436	16.00	60800	1	-	-	-	Spirals	0.80	50	356
	P2S2	150	300	0	30.04	GFRP	0.436	16.00	60800	2	-	-	-	Spirals	0.80	50	356
	P3S2	150	300	0	30.04	GFRP	0.436	16.00	60800	3	-	-	-	Spirals	0.80	50	356

Comb.	References	Mean	CV
1	Cusson and Paultre [2] and Samaan et al. [10]	0.97	0.22
2	Cusson and Paultre [2] and Miyauchi et al. [11]	1.05	0.20
3	Cusson and Paultre [2] and Kono et al. [12]	0.84	0.24
4	Cusson and Paultre [2] and Toutanji [13]	1.13	0.20
5	Cusson and Paultre [2] and Saafi et al. [14]	0.93	0.21
6	Cusson and Paultre [2] and Spoelstra and Monti [15]	0.93	0.20
7	Cusson and Paultre [2] and Fardis and Khalili [16]	0.86	0.21
8	Cusson and Paultre [2] and Karbhari and Eckel [17]	0.91	0.21
9	Cusson and Paultre [2] and Mirmiran and Shahawy [18]	0.80	0.26
10	Cusson and Paultre [2] and Shehata, Carneiro, and Shehata [19]	0.86	0.21
11	Saatcioglu and Razvi [3] and Samaan et al. [10]	1.06	0.21
12	Saatcioglu and Razvi [3] and Miyauchi et al. [11]	1.15	0.20
13	Saatcioglu and Razvi [3] and Kono et al. [12]	0.93	0.24
14	Saatcioglu and Razvi [3] and Toutanji [13]	1.22	0.20
15	Saatcioglu and Razvi [3] and Saafi et al. [14]	1.02	0.21
16	Saatcioglu and Razvi [3] and Spoelstra and Monti [15]	1.02	0.20
17	Saatcioglu and Razvi [3] and Fardis and Khalili [16]	0.95	0.21
18	Saatcioglu and Razvi [3] and Karbhari and Eckel [17]	1.00	0.21
19	Saatcioglu and Razvi [3] and Mirmiran and Shahawy [18]	0.89	0.26
20	Saatcioglu and Razvi [3] and Shehata, Carneiro, and Shehata [19]	0.95	0.21
21	Frangou et al. [4] and Samaan et al. [10]	0.96	0.22
22	Frangou et al. [4] and Miyauchi et al. [11]	1.04	0.21
23	Frangou et al. [4] and Kono et al. [12]	0.83	0.24
24	Frangou et al. [4] and Toutanji [13]	1.12	0.20
25	Frangou et al. [4] and Saafi et al. [14]	0.92	0.22
26	Frangou et al. [4] and Spoelstra and Monti [15]	0.92	0.20
27	Frangou et al. [4] and Fardis and Khalili [16]	0.85	0.22
28	Frangou et al. [4] and Karbhari and Eckel [17]	0.90	0.22
29	Frangou et al. [4] and Mirmiran and Shahawy [18]	0.79	0.26
30	Frangou et al. [4] and Shehata, Carneiro, and Shehata [19]	0.85	0.22
31	fib Model Code 2010 [5] and Samaan et al. [10]	1.00	0.21
32	fib Model Code 2010 [5] and Miyauchi et al. [11]	1.09	0.19
33	fib Model Code 2010 [5] and Kono et al. [12]	0.87	0.23
34	fib Model Code 2010 [5] and Toutanji [13]	1.16	0.19
35	fib Model Code 2010 [5] and Saafi et al. [14]	0.97	0.21
36	fib Model Code 2010 [5] and Spoelstra and Monti [15]	0.97	0.19
37	fib Model Code 2010 [5] and Fardis and Khalili [16]	0.90	0.21
38	fib Model Code 2010 [5] and Karbhari and Eckel [17]	0.94	0.21
39	fib Model Code 2010 [5] and Mirmiran and Shahawy [18]	0.83	0.25
40	fib Model Code 2010 [5] and Shehata, Carneiro, and Shehata [19]	0.89	0.21
41	Machado [9]	1.06	0.23

References	t
Cusson and Paultre [2] and Samaan et al. [10]	-0.12386
Cusson and Paultre [2] and Miyauchi et al. [11]	-3.05512
Cusson and Paultre [2] and Kono et al. [12]	5.66179
Cusson and Paultre [2] and Toutanji [13]	-4.95605
Cusson and Paultre [2] and Saafi et al. [14]	1.58771
Cusson and Paultre [2] and Spoelstra and Monti [15]	2.15434
Cusson and Paultre [2] and Fardis and Khalili [16]	5.33989
Cusson and Paultre [2] and Karbahari and Eckel [17]	2.77478
Cusson and Paultre [2] and Mirmiran and Shahawy [18]	6.74943
Cusson and Paultre [2] and Shehata, Carneiro and Shehata [19]	5.66797
Saatcioglu and Razvi [3] and Samaan et al. [10]	-2.85229
Saatcioglu and Razvi [3] and Miyauchi et al. [11]	-5.52444
Saatcioglu and Razvi [3] and Kono et al. [12]	1.99897
Saatcioglu and Razvi [3] and Toutanji [13]	-6.67271
Saatcioglu and Razvi [3] and Saafi et al. [14]	-1.78451
Saatcioglu and Razvi [3] and Spoelstra and Monti [15]	-1.72622
Saatcioglu and Razvi [3] and Fardis and Khalili [16]	0.73222
Saatcioglu and Razvi [3] and Karbahari and Eckel [17]	-0.96384
Saatcioglu and Razvi [3] and Mirmiran and Shahawy [18]	2.56853
Saatcioglu and Razvi [3] and Shehata, Carneiro and Shehata [19]	0.98920
Frangou et al. [4] and Samaan et al. [10]	0.23657
Frangou et al. [4] and Miyauchi et al. [11]	-2.70569
Frangou et al. [4] and Kono et al. [12]	6.19093
Frangou et al. [4] and Toutanji [13]	-4.71205
Frangou et al. [4] and Saafi et al. [14]	2.02394
Frangou et al. [4] and Spoelstra and Monti [15]	2.64534
Frangou et al. [4] and Fardis and Khalili [16]	5.87421
Frangou et al. [4] and Karbahari and Eckel [17]	3.24570
Frangou et al. [4] and Mirmiran and Shahawy [18]	7.20314
Frangou et al. [4] and Shehata, Carneiro, and Shehata [19]	6.20487
fib Model Code 2010 [5] and Samaan et al. [10]	-1.35751
fib Model Code 2010 [5] and Miyauchi et al. [11]	-4.28415
fib Model Code 2010 [5] and Kono et al. [12]	3.95378
fib Model Code 2010 [5] and Toutanji [13]	-5.88707
fib Model Code 2010 [5] and Saafi et al. [14]	0.13277
fib Model Code 2010 [5] and Spoelstra and Monti [15]	0.48751
fib Model Code 2010 [5] and Fardis and Khalili [16]	3.50500
fib Model Code 2010 [5] and Karbahari and Eckel [17]	1.20664
fib Model Code 2010 [5] and Mirmiran and Shahawy [18]	5.19730
fib Model Code 2010 [5] and Shehata, Carneiro and Shehata [19]	3.81781
Machado [9]	-2.85789