Reliability Analysis of FRP-Concrete-Steel Tubular Composite Column Under Axial Compression

doi:10.12068/j.issn.1005-3026.2024.03.016

Abstract

Abstract:

Several existing FRP-confined concrete strength models were evaluated by using 85 FRP?concrete?steel DSTC（double‐skin tubular column） axial compression test data as statistical samples. Finally， Teng’s model was selected for reliability analysis， and the optimal probability distributions of strength model error and resistance were determined. The reliability of DSTC was calculated using the JC method. The results show that the reliability index increases with the increase of steel tube strength， hollow ratio and steel ratio， while it is not significantly influenced by concrete strength. The increase in FRP confining stress leads to the decrease in reliability index. Based on the target reliability index of 3.7， a new expression of resistance partial factor is proposed for DSTC.

Key words: double skin tubular column（DSTC）, strength model, reliability analysis, JC method, resistance partial factor, fiber reinforced polymer

CLC Number:

TU 312.1

Hai-yang GAO, Lian-guang WANG, Bai-ling CHEN. Reliability Analysis of FRP-Concrete-Steel Tubular Composite Column Under Axial Compression[J]. Journal of Northeastern University(Natural Science), 2024, 45(3): 430-438.

Figures/Tables 13

Fig.1 Cross?section of FRP?concrete?steel DSTC

Table 1 Test data of FRP?concrete?steel DSTCs

数据来源	试件数量	D_o/mm	D_s/mm	t_s/mm	f_co/MPa	f_ys/MPa	FRP类型
文献[10]	6	152.5	76.1	3.2	39.64	352.67	GFRP
文献[11]	18	152.5	42~115	2.1~5.2	36.7~46.7	337.8~406.2	GFRP
文献[12]	8	194.6~195.3	114/140	2.5~8.16	29.3~32.5	313~363	GFRP/CFRP
文献[13]	6	401.0/402.0	245.8/323.6	8.0/9.3	29.3~40.1	307.2~316.3	GFRP
文献[14]	14	152.5	60.3~114.3	3.2~6.0	49.8/113.8	314.2~459.4	AFRP/CFRP
文献[15]	10	152.5	60.3~114.3	3.2~6.0	96.2	318.3~446.4	GFRP
文献[16]	12	204.4~320.0	120~219	4.5~6.0	40.9~104.4	319.4~419.5	GFRP
文献[17]	11	100	48	1.5~3.0	35.6~40.0	350.0~471.7	CFRP

Fig.2 Comparison of ultimate strengths from different models

Table 2 Calculation results of strength models of existing FRP?confined concrete

模型	极限强度	AV	SD	CV
Teng等^[1]	$f c c' f c o = 1 + 3.5 f l f c o$	0.987	0.124	0.127
Lignola等^[3]	$f c c' = f c o - 1.254 + 2.254 1 + 7.94 f l f c o - 2 f l f c o$	0.893	0.117	0.130
Yu等^[4]	$f c c' f c o = 1 + 3.5 ρ K - 0.01 ρ ε, ρ K ≥ 0.01 ρ K = E F R P t F R P f c o R o / ε c o, ρ ε = 0.586 ε r u ε c o$	1.184	0.163	0.137
Marques等^[18]	$f c c' = f c o + k 1 f l k 1 = 6.7 f l - 0.17$	0.913	0.118	0.128
Binici^[19]	$f c c' = f c o 1 + 9.9 f l f c o + f l f c o$	0.907	0.119	0.130
Xiao等^[20]	$f c c' f c o = 1 + 3.24 f l f c o 0.8$	0.919	0.123	0.132
Harries等^[21]	$f c c' = f c o + 4.269 f l 0.587$	1.211	0.196	0.161
Pham等^[22]	$f c c' = 0.91 f c o + 1.88 f l + 7.6 t F R P D o$	1.139	0.156	0.137

Table 2 Calculation results of strength models of existing FRP?confined concrete

模型	极限强度	AV	SD	CV
Teng等^[1]	$f c c' f c o = 1 + 3.5 f l f c o$	0.987	0.124	0.127
Lignola等^[3]	$f c c' = f c o - 1.254 + 2.254 1 + 7.94 f l f c o - 2 f l f c o$	0.893	0.117	0.130
Yu等^[4]	$f c c' f c o = 1 + 3.5 ρ K - 0.01 ρ ε, ρ K ≥ 0.01 ρ K = E F R P t F R P f c o R o / ε c o, ρ ε = 0.586 ε r u ε c o$	1.184	0.163	0.137
Marques等^[18]	$f c c' = f c o + k 1 f l k 1 = 6.7 f l - 0.17$	0.913	0.118	0.128
Binici^[19]	$f c c' = f c o 1 + 9.9 f l f c o + f l f c o$	0.907	0.119	0.130
Xiao等^[20]	$f c c' f c o = 1 + 3.24 f l f c o 0.8$	0.919	0.123	0.132
Harries等^[21]	$f c c' = f c o + 4.269 f l 0.587$	1.211	0.196	0.161
Pham等^[22]	$f c c' = 0.91 f c o + 1.88 f l + 7.6 t F R P D o$	1.139	0.156	0.137

Fig.3 Calculation model error histogram

Table 3 Uncertainty coefficient of design parameters

设计参数	均值系数	变异系数	概率分布类型
FRP壁厚t_FRP	1	0.02	正态
混凝土外径D_o	1	0.01	正态
混凝土面积A_c	1	0.05	正态
钢管面积A_s	1	0.05	正态
恒荷载S_G	1.060	0.070	正态
办公楼活荷载S_QO	0.524	0.288	极值I型
住宅楼活荷载S_QR	0.644	0.230	极值I型

Table 4 Uncertainty coefficient of material parameters

材料参数	钢材		材料参数	混凝土					FRP
材料参数	Q235	Q345	材料参数	C40	C50	C60	C70	C80	FRP
f_yk/MPa	235（ $t ≤ 16 ? m m$ ） 225（ $t > 16 ? m m$ ）	345（ $t ≤ 16 ? m m$ ） 335（ $t > 16 ? m m$ ）	f_ck/MPa	26.8	32.4	38.5	44.5	50.2	—
f_ys/MPa	215（ $t ≤ 16 ? m m$ ） 205（ $t > 16 ? m m$ ）	305（ $t ≤ 16 ? m m$ ） 295（ $t > 16 ? m m$ ）	f_co/MPa	19.1	23.1	27.5	31.8	35.9	—
均值系数	1.08	1.09	均值系数	1.342	1.337	1.332	1.292	1.262	1.1
变异系数	0.08	0.07	变异系数	0.156	0.149	0.141	0.121	0.101	0.083
概率分布类型	对数正态		概率分布类型	正态					威布尔

Table 4 Uncertainty coefficient of material parameters

材料参数	钢材		材料参数	混凝土					FRP
材料参数	Q235	Q345	材料参数	C40	C50	C60	C70	C80	FRP
f_yk/MPa	235（ $t ≤ 16 ? m m$ ） 225（ $t > 16 ? m m$ ）	345（ $t ≤ 16 ? m m$ ） 335（ $t > 16 ? m m$ ）	f_ck/MPa	26.8	32.4	38.5	44.5	50.2	—
f_ys/MPa	215（ $t ≤ 16 ? m m$ ） 205（ $t > 16 ? m m$ ）	305（ $t ≤ 16 ? m m$ ） 295（ $t > 16 ? m m$ ）	f_co/MPa	19.1	23.1	27.5	31.8	35.9	—
均值系数	1.08	1.09	均值系数	1.342	1.337	1.332	1.292	1.262	1.1
变异系数	0.08	0.07	变异系数	0.156	0.149	0.141	0.121	0.101	0.083
概率分布类型	对数正态		概率分布类型	正态					威布尔

Fig.4 Optimal probability distribution of resistance

Fig.5 Influence of concrete and steel tube strengths on reliability index of the composite member

Fig.6 Influence of hollow ratio and steel ratio on reliability index of the composite member

Fig.7 Influence of load effect ratio on reliability index of the composite member

Fig.8 Influence of FRP confining stress on reliability index of the composite member

Fig.9 Influence of FRP confining stress and load effect ratio on resistance partial factor

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