混杂配筋(钢和FRP筋)梁正截面受弯设计方法研究

杨洋; 潘登; 吴刚; 曹大富; 陆伟刚

doi:10.6052/j.issn.1000-4750.2020.09.0703

混杂配筋(钢和FRP筋)梁正截面受弯设计方法研究

doi: 10.6052/j.issn.1000-4750.2020.09.0703

杨洋^1,,
潘登^1,,
吴刚^2, ,,
曹大富^1,,
陆伟刚^3,

1.
扬州大学建筑科学与工程学院，江苏，扬州 225127
2.
东南大学土木工程学院，江苏，南京 210096
3.
扬州大学水利科学与工程学院，江苏，扬州 225127

基金项目: 江苏省自然科学基金青年基金项目(BK20180931)；国家自然科学基金青年基金项目(51908486)；中国博士后基金项目(2020M671620)；江苏省博士后科研资助计划项目(2020Z290)

详细信息

作者简介:
杨　洋(1985−)，男，江苏盐城人，讲师，博士，硕导，主要从事结构工程研究 (E-mail: y.yang@yzu.edu.cn)

潘　登(1993−)，男，江苏宿迁人，硕士，主要从事结构工程研究 (E-mail: 360605456@qq.com)

曹大富(1964−)，男，江苏扬州人，教授，博士，博导，主要从事工程结构加固与改造研究 (E-mail: dfcao@yzu.edu.cn)

陆伟刚(1964−)，男，江苏苏州人，教授，博士，博导，主要从事水工结构及水力学研究 (E-mail: wglu@yzu.edu.cn)

通讯作者:
吴　刚(1976−)，男，浙江安阳人，教授，博士，博导，主要从事结构工程研究 (E-mail: g.wu@seu.edu.cn)

中图分类号: TU375.1
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- 被引次数: 0
出版历程
- 收稿日期: 2020-09-29
- 修回日期: 2021-04-07
- 网络出版日期: 2021-04-22
- 刊出日期: 2021-09-13

DESIGN METHOD FOR NORMAL SECTION OF HYBRID REINFORCED (STEEL AND FRP BARS) BEAMS UNDER BENDING

YANG Yang^1
,,
PAN Deng^1
,,
WU Gang^{2
, ,},
CAO Da-fu^1
,,
LU Wei-gang^3
,

1.
College of Civil Science and Engineering, Yangzhou University, Yangzhou, Jiangsu 225127, China
2.
School of Civil Engineering, Southeast University, Nanjing, Jiangsu 210096, China
3.
College of Hydraulic Science and Engineering, Yangzhou University, Yangzhou, Jiangsu 225127, China

摘要

摘要: 钢和纤维复合筋混杂增强混凝土(hybrid reinforced concrete，Hybrid-RC)梁具有较好的承载力、耐久性和延性。然而，基于文献调研发现，现有设计方法对Hybrid-RC梁正截面受弯的破坏形态还未能做出准确的预测。因此，该文修正了现有的设计方法，并通过数据库对比，验证了其有效性。在此基础上，对Hybrid-RC梁提出了一种新的设计思路，以减少使用成本，并得到更高的使用荷载。
- 混杂配筋(Hybrid-RC)梁 /
- 破坏形态 /
- 抗弯承载力 /
- 设计程序 /
- 数值模拟
Abstract: The hybrid reinforced concrete (Hybrid-RC) beam consisting steel bars and fiber-reinforced polymer bars can provide better bearing capacity, durability and ductility. However, literature review showed that the design methods for the normal section of Hybrid-RC beams under bending failed to predict the failure mode of these structures accurately. Therefore, it revises the existing design method, and verifies its effectiveness through database comparison. On this basis, a new design idea of Hybrid-RC beam is proposed to reduce the service cost and achieve higher service load.
- hybrid reinforced concrete (Hybrid-RC) beam /
- failure mode /
- flexural capacity /
- design procedure /
- numerical simulation

HTML全文

图 1 Hybrid-RC梁受弯破坏形态及应变分布

Figure 1. The failure mode and strain distribution of the Hybrid-RC beam under bending

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图 2 等效矩形应力图

Figure 2. Equivalent rectangular stress diagram

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图 3 程序设计流程图

Figure 3. Design procedure

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图 4 ABAQUS有限元模型

Figure 4. ABAQUS finite element model

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图 5 混凝土的本构关系

Figure 5. Constitutive relation of concrete

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图 6 钢筋和FRP筋的应力-应变关系

Figure 6. Stress-strain relationship of the steel bar and FRP

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图 7 试验梁与ABAQUS模拟梁的荷载-挠度曲线

Figure 7. Load-deflection curves of test beams and ABAQUS simulated beams

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图 8 ABAQUS模拟梁的荷载-挠度曲线

Figure 8. Load-deflection curves of the ABAQUS simulated beams

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表 1 文献中混杂配筋梁的截面参数

Table 1. Cross section parameters of hybrid-RC beams in the literature

文献	梁号	b/mm	d/mm	$f_{\rm{c}}' /{\rm{MPa}}$	A_f/mm²	A_s/mm²	f_y/MPa	f_fu/MPa	E_f/GPa	破坏形态
Qu等^[20]	B3	180	206	26.48	253.23	226.08	363.0	782	45.0	A
	B4	180	204	26.48	396.91	200.96	336.0	755	41.0	A
	B5	180	206	27.52	141.69	401.92	336.0	778	37.7	A
	B6	180	204	27.52	253.23	401.92	336.0	782	45.0	A
	B7	180	208	32.52	141.69	113.04	363.0	778	37.7	A
	B8	180	197	32.52	396.91	1205.76	336.0	755	41.0	A
Aiello和Ombres^[12]	A1	150	175	45.70	88.31	100.48	465.0	1674	49.0	A
	A2	150	175	45.70	157.00	100.48	465.0	1366	50.1	A
	A3	150	175	45.70	235.50	226.08	465.0	1366	50.1	A
	C1	150	175	45.70	88.31	100.48	465.0	1674	49.0	A
LauDenvid^[22]	G10T07	280	348	39.80	981.70	628.30	597.0	582	38.0	A
LauDenvid^[22]	G06T1	280	351	44.60	567.10	981.70	550.0	588	39.5	A
Safan^[26]	B10/6S	100	136	30.00	56.60	157.00	530.0	780	41.0	A
	B10/8S	100	136	30.00	100.60	157.00	530.0	755	39.0	A
	B12/6S	100	135	30.00	56.60	226.00	470.0	780	41.0	A
	B12/8S	100	135	30.00	100.60	226.00	470.0	755	39.0	A
Leung 和 Balendran^[17]	L2	150	145	28.50	142.60	157.00	460.0	760	40.8	A
	L5	150	145	28.50	213.90	157.00	460.0	760	40.8	A
	H2	150	145	48.80	142.60	157.00	460.0	760	40.8	A
	H5	150	145	48.80	213.90	157.00	460.0	760	40.8	A
Al-Mahmoud^[27]	SC-12	150	254	35.10	113.00	226.00	600.0	1875	146.0	A
LauDenvid^[22]	G03MD1	280	351	41.30	283.50	981.70	336.0	588	39.5	B
Almusallam等^[28]	RW1F	150	170	36.60	78.50	157.00	408.0	743	40.0	B
Rahimi 和 Hutchinson^[29]	RHB3	200	135	52.30	66.00	157.00	575.0	1532	127.0	B
Tan^[16]	B2	200	375	28.24	25.12	150.70	324.4	1776	52.0	B
Nguyen等^[30]	B2	120	140	35.68	96.00	628.30	466.0	3140	181.0	C
Xiong等^[31]	CF1	120	130	15.68	8.11	226.20	569.0	3652	252.0	C
Xiong^[32]	CF3	80	110	15.68	5.11	226.20	346.7	3652	252.0	C
注：A表示钢筋屈服后混凝土压溃；B表示钢筋屈服后FRP断裂；C表示的破坏形态为混凝土压溃，钢筋未屈服(但实际出现剥离破坏)。

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表 2 文献中混杂配筋梁试验值和理论值的对比

Table 2. Comparison between experimental and theoretical values of the tested hybrid-RC beams

梁号	Qu^[20]			Lau^[22]			提出的等刚度配筋			提出的等强度配筋			M_exp/ (kN·m)	M_s,th/ (kN·m)	M_f,th/ (kN·m)	M_exp/M_th
梁号	$\rho_{\rm{eff}}^1 $/ (%)	$\rho_{\rm{eff,b}}^1 $/ (%)	PFM	$\rho_{\rm{eff}}^2 $/ (%)	$\rho_{\rm{eff,b}}^2 $/ (%)	PFM	$\rho_{\rm{s}}^{\rm{e}} $/ (%)	($\rho_{{\rm{s,b}}{\text{-}}{\text{Ⅰ}} }^{\rm{e}} $, $\rho_{{\rm{s,b}}{\text{-}}{\text{Ⅱ}} }^{\rm{e}} $)/ (%)	PFM	$\rho_{\rm{f}}^{\rm{e}} $/ (%)	($\rho_{{\rm{f,b}}{\text{-}}{\text{Ⅰ}} }^{\rm{e}} $, $\rho_{{\rm{f,b}}{\text{-}}{\text{Ⅱ}} }^{\rm{e}} $)/ (%)	PFM	M_exp/ (kN·m)	M_s,th/ (kN·m)	M_f,th/ (kN·m)	M_exp/M_th
B3	0.76	3.57	A	0.97	0.44	A	0.76	(0.35,3.57)	A	0.97	(0.44,4.51)	A	38.38	35.59	35.59	1.08
B4	0.77	3.95	A	1.32	0.43	A	0.77	(0.25,3.95)	A	1.32	(0.43,6.80)	A	39.66	37.59	37.59	1.06
B5	1.16	4.10	A	0.85	0.40	A	1.16	(0.54,4.10)	A	0.85	(0.40,3.02)	A	36.36	35.25	35.25	1.03
B6	1.25	4.10	A	1.16	0.46	A	1.25	(0.49,4.10)	A	1.16	(0.46,3.82)	A	42.57	40.56	40.56	1.05
B7	0.37	4.21	A	0.52	0.45	A	0.37	(0.32,4.21)	A	0.52	(0.45,5.86)	A	23.55	27.48	27.48	0.86
B8	3.63	4.66	A	2.63	0.51	A	3.63	(0.71,4.66)	A	2.63	(0.51,3.38)	A	63.30	68.60	68.60	0.92
A1	0.47	3.75	A	0.44	0.17	A	0.47	(0.18,3.75)	A	0.44	(0.17,3.57)	A	25.14	20.74	20.74	1.21
A2	0.53	3.75	A	0.73	0.25	A	0.53	(0.18,3.75)	A	0.73	(0.25,5.13)	A	28.41	25.38	25.38	1.12
A3	1.09	3.75	A	1.19	0.25	A	1.09	(0.23,3.75)	A	1.19	(0.25,4.11)	A	35.55	33.59	33.59	1.06
C1	0.47	3.75	A	0.44	0.17	A	0.47	(0.18,3.75)	A	0.44	(0.17,3.57)	A	25.14	20.74	20.74	1.21
G10T07	0.85	2.38	A	1.67	0.88	A	0.85	(0.45,2.38)	A	1.67	(0.88,4.68)	A	261	224.86	224.86	1.16
G06T1	1.11	2.90	A	1.51	0.96	A	1.11	(0.71,2.90)	A	1.51	(0.96,3.93)	A	229	239.56	239.56	0.96
B10/6S	1.24	2.37	A	1.20	0.45	A	1.24	(0.47,2.37)	A	1.20	(0.45,2.29)	A	14.09	11.64	11.64	1.21
B10/8S	1.3	2.37	A	1.55	0.46	A	1.30	(0.39,2.37)	A	1.55	(0.46,2.83)	A	14.41	12.42	12.42	1.16
B12/6S	1.76	2.80	A	1.43	0.45	A	1.76	(0.56,2.80)	A	1.43	(0.45,2.27)	A	14.89	13.27	13.27	1.12
B12/8S	1.82	2.80	A	1.79	0.46	A	1.82	(0.47,2.80)	A	1.79	(0.46,2.75)	A	16.33	13.85	13.85	1.18
L2	0.86	2.78	A	1.09	0.46	A	0.86	(0.36,2.78)	A	1.09	(0.46,3.55)	A	22.23	16.25	16.25	1.37
L5	0.92	2.78	A	1.42	0.46	A	0.92	(0.30,2.78)	A	1.42	(0.46,4.28)	A	23.07	17.89	17.89	1.29
H2	0.86	3.94	A	1.09	0.65	A	0.86	(0.51,3.94)	A	1.09	(0.65,5.03)	A	21.11	19.45	19.45	1.09
H5	0.92	3.94	A	1.42	0.65	A	0.92	(0.42,3.94)	A	1.42	(0.65,6.07)	A	27.06	21.82	21.82	1.24
SC-12	0.80	2.27	A	0.49	0.29	A	0.80	(0.48,2.27)	A	0.49	(0.29,1.38)	A	65.4	61.96	61.96	1.06
G03MD1	1.06	5.30	Fail	0.86	0.92	B	1.06	(1.13,5.30)	B	0.86	(0.92,4.29)	B	147.7	164.66	164.66	0.90
RW1F	0.68	3.91	A	0.65	0.56	A	0.68	(0.59,3.91)	A	0.65	(0.56,3.73)	A	21.84	18.32	18.32	1.19
RHB3	0.73	3.04	Fail	0.46	0.47	B	0.73	(0.74,3.04)	B	0.46	(0.47,1.93)	B	20.7	23.92	23.92	0.87
B2	0.21	4.40	Fail	0.07	0.11	B	0.21	(0.34,4.40)	B	0.07	(0.11,1.47)	B	35.25	40.61	40.61	0.87
B2	4.26	3.21	C	1.13	0.14	Fail	4.26	(0.52,3.21)	C	1.13	(0.14,0.85)	C	28.6	30.33	30.33	0.94
CF1	1.52	1.14	C	0.28	0.06	Fail	1.52	(0.35,1. 14)	C	0.28	(0.06,0.21)	C	15.42	11.68	11.68	1.32
CF3	2.64	2.24	C	0.3	0.06	Fail	2.64	(0.56,2.24)	C	0.3	(0.06,0.26)	C	6.09	5.79	5.79	1.05
注：PFM表示预测的破坏形态；A表示钢筋屈服后混凝土压溃；B表示钢筋屈服后FRP断裂；C表示为混凝土压溃，钢筋未屈服；Fail表示未出现预测的破坏形态。

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表 3 设计混杂梁的截面参数

Table 3. Cross section parameters of the designed hybrid-RC beams

梁号	b/mm	d/mm	$ f_{\rm{c}}' $/MPa	A_f/mm²	A_s/mm²	f_y/MPa	f_fu/MPa	E_f/GPa	M_th/(kN·m)	A_f /A_s
B4	180	204	26.48	396.91	200.96	336	755	41.0	37.59	1.98
B4-1	180	204	26.48	221.01	452.39	336	755	41.0	39.66	0.49
B4-2	180	204	26.48	163.52	508.94	336	755	41.0	39.66	0.32
B4-3	180	204	26.48	42.19	628.32	336	755	41.0	39.66	0.07
G03MD1	280	351	41.30	283.50	981.70	336	588	39.5	−	−
G03MD1-1	280	351	20.00	74.10	1407.40	336	588	39.5	147.70	0.05
G03MD1-2	280	280	41.30	133.60	1608.50	336	588	39.5	147.70	0.08
G03MD1-3	280	351	41.30	31.20	1256.60	336	1675	49.0	147.70	0.02
B2	120	140	35.68	96.00	628.30	466	3140	181.0	−	−
B2-1	120	140	60.00	30.66	452.39	466	3140	181.0	28.60	0.07
B2-2	120	180	35.68	21.55	339.29	466	3140	181.0	28.60	0.06
B2-3	120	140	35.68	85.10	804.25	300	3140	181.0	28.60	0.11

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表 4 模拟混杂梁的截面参数

Table 4. Cross section parameters of the Abaqus simulated hybrid-RC beams

梁号	b/mm	d/mm	$f_{\rm{c}}' $/MPa	A_f/mm²	A_s/mm²	f_y/MPa	f_fu/MPa	E_f/GPa	A_f /A_s	Δ_u/Δ_y
B3	180	206	26.48	253.23	226.08	363	782	45.0	1.12	5.18
B3-1	180	206	26.48	73.20	508.68	363	782	45.0	0.14	3.11
B6	180	204	27.52	253.23	401.92	336	782	45.0	0.63	4.38
B6-1	180	204	27.52	93.25	628.32	336	782	45.0	0.15	3.07
B7	180	208	32.52	141.69	113.04	363	778	37.7	1.25	6.51
B7-1	180	208	32.52	54.62	200.96	363	778	37.7	0.27	4.93
C1	150	175	45.70	88.31	100.48	465	1674	49.0	0.88	6.35
C1-1	150	175	45.70	49.50	226.19	465	1674	49.0	0.22	4.69

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