1 Introduction
2 Experimental Program
2.1 General
-
Two heat-damaged specimens in each of the two groups CH2 (heated for 2 h) and CH3 (heated for 3 h) were wrapped using CFRP sheets: specimen CHi-C1L wrapped with a single layer and specimen CHi-C2L wrapped with two layers of the fabric sheets where the subscript i indicates the heating duration in hours. According to ACI 440.2R (2008) the CFRP sheets, with a thickness of 0.131 mm, provide an FRP reinforcement ratio of 0.00273 and 0.00546 for the single and double layer wraps, respectively.
-
Two heat-damaged specimens in each of the two groups CH2 and CH3 were confined using glass fiber reinforced polymer (GFRP) sheets: specimens CHi-G1L and CHi-G2L were wrapped using one and two layers of the 0.17 mm thick sheets, respectively. According to ACI 440.2R (2008), the single and double layer GFRP wraps provide an FRP reinforcement ratio of 0.00354 and 0.00708, respectively.
Specimen designation | Heating duration (h) | Wrapping scheme | Notes | |
---|---|---|---|---|
CFRP layers | GFRP layers | |||
Control CH0-A | 0 | 0 | 0 | Unheated; unwrapped |
Control CH0-B | 0 | 0 | 0 | Unheated; unwrapped |
Control CH0-C1L | 0 | 1 | 0 | Unheated; wrapped with 1 layer of CFRP |
Control CH2-A | 2 | 0 | 0 | Heated (2 h); unwrapped |
Control CH2-B | 2 | 0 | 0 | Heated (2 h); unwrapped |
Control CH3-A | 3 | 0 | 0 | Heated (3 h); unwrapped |
Control CH3-B | 3 | 0 | 0 | Heated (3 h); unwrapped |
CH2-C1L | 2 | 1 | 0 | Heated (2 h); wrapped with 1 layer of CFRP |
CH2-C2L | 2 | 2 | 0 | Heated (2 h); wrapped with 2 layers of CFRP |
CH2-G1L | 2 | 0 | 1 | Heated (2 h); wrapped with 1 layer of GFRP |
CH2-G2L | 2 | 0 | 2 | Heated (2 h); wrapped with 2 layers of GFRP |
CH3-C1L | 3 | 1 | 0 | Heated (3 h); wrapped with 1 layer of CFRP |
CH3-C2L | 3 | 2 | 0 | Heated (3 h); wrapped with 2 layers of CFRP |
CH3-G1L | 3 | 0 | 1 | Heated (3 h); wrapped with 1 layer of GFRP |
CH3-G2L | 3 | 0 | 2 | Heated (3 h); wrapped with 2 layers of GFRP |
2.2 Layout and Detailing of Test Specimens
2.3 Materials
Type of sheets | CFRP | GFRP |
---|---|---|
Width (mm) | 300 | 500 |
Thickness (mm) | 0.131 | 0.17 |
Areal weight (g/m2) | 230 ± 10 | 455 ± 22 |
Nominal tensile strength (MPa) | 4300 | 2300 |
Nominal tensile E-modulus (MPa) | 238,000 | 76,000 |
Nominal strain at break (%) | 1.8 | 2.8 |
2.4 Specimen-Preparation
2.5 Test Setup and Instrumentation
3 Test Results
3.1 General
Specimen | Axial stress (MPa) | Strain at peak stress | |
---|---|---|---|
Axial | Hoop | ||
Control CH0-A Control CH0-B | 34.2 | 0.00086 | 0.00057 |
Control CH2-A Control CH2-B | 18.5 (54.1)a
| 0.00145 (168.6) | 0.00080 (140.4) |
Control CH3-A Control CH3-B | 15.8 (46.2)a
| 0.00176 (204.7) | 0.00095 (166.7) |
CH0-C1L | 47.8 (139.8)a
| 0.00416 (483.7) | 0.00413 (724.6) |
CH2-C1L | 37.9 (204.9)b
| 0.00776 (535.2) | 0.00466 (582.5) |
CH2-C2L | 47.1 (254.6)b
| 0.00910 (627.6) | 0.00892 (1115.0) |
CH3-C1L | 33.7 (213.3)c
| 0.00619 (351.7) | 0.00449 (472.6) |
CH3-C2L | 46.0 (291.1)c
| 0.00831 (472.2) | 0.00829 (872.6) |
CH2-G1L | 27.3 (147.6)b
| 0.00527 (363.5) | 0.00518 (647.5) |
CH2-G2L | 36.1 (195.1)b
| 0.00555 (382.8) | 0.00551 (688.8) |
CH3-G1L | 27.1 (171.5)c
| 0.00537 (305.1) | 0.00444 (467.4) |
CH3-G2L | 30.3 (191.8)c
| 0.00558 (317.1) | 0.00521 (548.4) |
3.2 Failure Modes
3.3 Heat-Damaged Specimens
Specimen |
F
u
(kN) | Secant stiffness (kN·mm) |
∆
max
(mm) | Toughness (kN·mm) | Ductility |
---|---|---|---|---|---|
Control CH0-A Control CH0-B | 989.1 | 2764.9 | 0.41 | 227 | 1.19 |
Control CH2-A Control CH2-B | 535.7 (54.2)a
| 870.0 (31.5) | 0.87 (212.2) | 293 (129.1) | 1.46 (122.7) |
Control CH3-A Control CH3-B | 458.5 (46.4)a
| 719.0 (26) | 1.06 (258.5) | 321.9 (142.1) | 1.62 (136.1) |
CH0-C1L | 1384.5 (140)a
| 1548.5 (56) | 2.02 (492.7) | 2097.2 (923.9) | 2.37 (199.2) |
CH2-C1L | 1096.1 (204.6)b
| 587.6 (67.5) | 3.49 (401.2) | 2550 (870.3) | 2.94 (201.4) |
CH2-C2L | 1364.5 (254.7)b
| 638.3 (73.4) | 4.10 (471.3) | 3822 (1304.4) | 2.58 (176.7) |
CH3-C1L | 975.1 (212.7)c
| 548.7 (76.3) | 2.79 (263.2) | 1701 (528.4) | 3.00 (185.2) |
CH3-C2L | 1332.5 (290.6)c
| 570.1 (79.3) | 3.74 (352.8) | 3100 (963.0) | 2.61 (161.1) |
CH2-G1L | 790.5 (147.6)b
| 539.6 (62) | 2.46 (282.8) | 1286 (438.9) | 2.07 (141.8) |
CH2-G2L | 1045.3 (195.1)b
| 603.4 (69.4) | 2.53 (290.8) | 1670 (570.0) | 1.72 (117.8) |
CH3-G1L | 783.6 (170.9)c
| 472.0 (65.6) | 2.43 (229.3) | 1179 (366.3) | 2.00 (123.5) |
CH3-G2L | 876.4 (191.1)c
| 539.9 (75.1) | 2.61 (246.2) | 1488 (462.2) | 1.95 (120.4) |
Control specimens |
F
u
(kN) |
P
o
(kN) |
E
c
|
I
|
EI
(N·mm2) |
P
c
(kN) |
---|---|---|---|---|---|---|
CH0-A CH0-B | 989a
| 1484b
|
\( 4700\,\sqrt {f_{c}^{'} } \)
|
I
g
| 4.52 × 1011
| 8616b
|
CH2-A CH2-B | 536 | 693 |
\( 2820\;\sqrt {f_{c}^{'} } \)
| 0.7I
g
| 1.90 × 1011
| 3619 |
CH3-A CH3-B | 459 | 620 |
\( 2820\;\sqrt {f_{c}^{'} } \)
| 0.7I
g
| 1.90 × 1011
| 3619 |
3.4 Repaired Heat-Damaged Columns
3.4.1 Columns Repaired Using CFRP Sheets
3.4.2 Columns Repaired Using GFRP Sheets
4 Theoretical Strength Predictions of FRP-Confined Columns
Model | Concrete confined strength | Confining pressure | |
---|---|---|---|
ACI 440.2R (2008) |
\( f_{cc}^{'} = f_{c}^{'} + \psi_{f} 3.3f_{l} \)
\( f_{cc}^{'} = f_{c}^{'} \)
| if \( \frac{{f_{l} }}{{f_{c}^{'} }}\;\; \ge \;\;0.08 \)
if \( \frac{{f_{l} }}{{f_{c}^{'} }}\;\; < \;\;0.08 \)
|
\( \psi_{f} = \;0.95 \)
\( f_{l} = \frac{{2E_{f} nt_{f} \varepsilon_{fe} }}{D} \)
\( \varepsilon_{fe} = 0.55\,\varepsilon_{fu} \)
|
CNR (2013) |
\( \frac{{f_{cc}^{'} }}{{f_{c}^{'} }} = 1\; + \;2.6\left( {\frac{{f_{l,eff} }}{{f_{c}^{'} }}} \right)^{2/3} \)
\( \frac{{f_{cc}^{'} }}{{f_{c}^{'} }} = 1 \)
| if \( \frac{{f_{l,eff} }}{{f_{c}^{'} }}\;\; > \;\;0.05 \)
if \( \frac{{f_{l,eff} }}{{f_{c}^{'} }}\;\; \le \;\;0.05 \)
|
\( f_{l,eff} \;\; = \;\;\frac{{2E_{f} nt_{f} \varepsilon_{fd,rid} }}{D} \)
\( \varepsilon_{fd,rid} = \;\;\hbox{min} \{ \eta_{a} \;\varepsilon_{fu} /\gamma_{f} ;\;0.004\} \)
|
Lam and Teng (2003) |
\( \frac{{f_{cc}^{'} }}{{f_{co}^{'} }} = \;\;1\,\; + \;3.3\frac{{f_{l,a} }}{{f_{co}^{'} }} \)
\( \frac{{f_{cc}^{'} }}{{f_{co}^{'} }} = \;\;1 \)
| if \( \frac{{f_{l,a} }}{{f_{co}^{'} }}\,\,\, \ge \,\;0.07 \)
if \( \frac{{f_{l,a} }}{{f_{co}^{'} }}\;\; < \;\;0.07 \)
|
\( f_{l,a} \;\; = \;\;\frac{{2E_{f} t_{f} \varepsilon_{h,rup} }}{D} \)
for CFRP, \( \varepsilon_{h,rup} = \;\,0.586\;{\kern 1pt} \varepsilon_{fu} \)
for GFRP, \( \varepsilon_{h,rup} = \;\;0.624\;\varepsilon_{fu} \)
|
Teng et al. (2009) |
\( \frac{{f_{cc}^{'} }}{{f_{co}^{'} }}\;\; = \;\;1 + 3.5\left( {\rho_{k} - 0.01} \right)\rho_{\varepsilon } \)
\( \frac{{f_{cc}^{'} }}{{f_{co}^{'} }}\;\; = \;\;1 \)
| if \( \rho_{k} \;\; \ge \;\;0.01 \)
if \( \rho_{k} \;\; < \;\;0.01 \)
|
\( \rho_{k} = \;\;\frac{{2E_{f} t_{f} }}{{\left( {f_{co}^{'} /\varepsilon_{co} } \right)D}} \)
\( \rho_{\varepsilon } = \;\;\frac{{\varepsilon_{h,rup} }}{{\varepsilon_{co} }} \), \( \varepsilon_{co} = \;\;0.002 \)
|
Wu and Wang (2009) |
\( \frac{{f_{cc}^{'} }}{{f_{co}^{'} }} = 1\; + \;2.23\left( {\frac{{f_{lu} }}{{f_{co}^{'} }}} \right)^{0.96} \)
|
\( f_{lu} = \;\;\frac{{2f_{f} nt_{f} }}{D} \)
| |
Fahmy and Wu (2010) |
\( f_{cc}^{'} = f_{co}^{'} \; + \;k_{1} f_{lu} \)
\( k_{1} = 4.5f_{lu}^{ - 0.3} \) if \( f_{co}^{'} \;\; \le \;\;40{\kern 1pt} \;{\text{MPa}} \)
\( k_{1} = 3.75f_{lu}^{ - 0.3} \) if \( f_{co}^{'} > \;40{\kern 1pt} \;{\text{MPa}} \)
|
\( f_{lu} = \frac{{2f_{f} nt_{f} }}{D} \)
| |
Ozbakkaloglu and Lim (2013) |
\( f_{cc}^{'} = c_{1} f_{co}^{'} + 3.2\,\left( {f_{l,a} - f_{lo} } \right) \)
\( c_{1} = 1 + 0.0058\frac{{E_{l} }}{{f_{co}^{'} }} \)
\( f_{lo} = E_{l} \varepsilon_{l1} \)
|
\( \varepsilon_{l1} = \;\;\left( {0.43 + 0.009\frac{{E_{l} }}{{f_{co}^{'} }}} \right)\,\varepsilon_{co} \)
and \( E_{l} \,\ge \,f_{co}^{'\;1.65} \)
| |
Pham and Hadi (2014) |
\( f_{cc}^{'} = 0.91f_{co}^{'} + 1.88f_{l} + 7.6\frac{{t_{f} }}{D} \)
|
\( f_{l} = \frac{{2E_{f} nt_{f} \varepsilon_{fu} }}{D} \)
|
Specimen |
F
u
(kN) | ACI 440.2R (2008) | CNR (2013) | Lam and Teng (2003) | Teng et al. (2009) | Wu and Wang (2009) | Fahmy and Wu (2010) | Ozbakkaloglu and Lim (2013) | Pham and Hadi (2014) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
F
th
(kN) | (%) Error |
F
th
(kN) | (%) Error |
F
th
(kN) | (%) Error |
F
th
(kN) | (%) Error |
F
th
(kN) | (%) Error |
F
th
(kN) | (%) Error |
F
th
(kN) | (%) Error |
F
th
(kN) | (%) Error | ||
CH0-C1L | 1385 | 1483 | 7.1 | 1570 | 13.4 | 1568 | 13.2 | 1389 | 0.3 | 1504 | 8.6 | 1513 | 9.3 | 1599 | 15.5 | 1464 | 5.8 |
CH2-C1L | 1096 | 936 | −14.6 | 941 | −14.2 | 895 | −18.3 | 843 | −23.1 | 823 | −24.9 | 884 | −19.4 | 953 | −13.0 | 852 | −22.3 |
CH2-C2L | 1365 | 1180 | −13.5 | 1067 | −21.8 | 1169 | −14.4 | 1140 | −16.5 | 1013 | −25.7 | 1047 | −23.2 | 1271 | −6.8 | 1118 | −18.1 |
CH3-C1L | 975 | 864 | −11.4 | 854 | −12.4 | 832 | −14.7 | 789 | −19.1 | 758 | −22.2 | 820 | −15.9 | 892 | −8.5 | 793 | −18.7 |
CH3-C2L | 1333 | 1107 | −16.9 | 975 | −26.8 | 1105 | −17.1 | 1086 | −18.5 | 948 | −28.9 | 984 | −26.2 | 1210 | −9.2 | 1059 | −20.6 |
CH2-G1L | 791 | 850 | 7.5 | 725 | −8.2 | 809 | 2.4 | 695 | −12.0 | 754 | −4.6 | 814 | 3.0 | 862 | 9.1 | 757 | −4.2 |
CH2-G2L | 1045 | 1007 | −3.7 | 915 | −12.4 | 997 | −4.6 | 887 | −15.2 | 879 | −15.9 | 935 | −10.6 | 1100 | 5.2 | 929 | −11.2 |
CH3-G1L | 784 | 777 | −0.8 | 648 | −17.2 | 746 | −4.8 | 647 | −17.5 | 690 | −12.0 | 751 | −4.2 | 800 | 2.1 | 698 | −10.9 |
CH3-G2L | 876 | 934 | 6.6 | 830 | −5.3 | 934 | 6.5 | 838 | −4.4 | 814 | −7.2 | 871 | −0.6 | 1039 | 18.6 | 870 | −0.8 |