GFRP管−灌浆料修复锈蚀钢管节点受压性能研究

常鸿飞; 高宇航; 左文康; 李照伟; 严晓宇

doi:10.6052/j.issn.1000-4750.2021.08.0644

GFRP管−灌浆料修复锈蚀钢管节点受压性能研究

doi: 10.6052/j.issn.1000-4750.2021.08.0644

常鸿飞^{1, 2,},
高宇航^1,,
左文康^{1, 3, ,},
李照伟^1,,
严晓宇^1,

1.
中国矿业大学江苏省土木工程环境灾变与结构可靠性重点实验室，江苏，徐州 221116
2.
中国矿业大学深部岩土力学与地下工程国家重点实验室，江苏，徐州 221116
3.
上海交通大学船舶海洋与建筑工程学院，上海 200240

基金项目: 国家自然科学基金项目(51408596，51978657)；中央高校基本业务费项目(2021ZDPY0209)；徐州市重点研发计划项目(KC19199)

详细信息

作者简介:
常鸿飞(1982−)，男，河南信阳人，教授，博士，博导，主要从事钢结构加固修复研究(E-mail: honfee@126.com)

高宇航(1998−)，男，河北张家口人，硕士生，主要从事FRP组合结构研究(E-mail: 345387379@qq.com)

李照伟(1996−)，男，山东日照人，博士生，主要从事钢结构加固修复研究(E-mail: lzw1024913@163.com)

严晓宇(1999−)，男，湖北荆州人，本科生，主要从事FRP组合结构研究(E-mail: 759360786@qq.com)

通讯作者:
左文康(1995−)，男，江苏盐城人，博士生，主要从事钢结构加固修复与FRP组合结构研究(E-mail: zuowk@outlook.com)

中图分类号: TU391；TU317+.1
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- 被引次数: 0
出版历程
- 收稿日期: 2021-08-19
- 录用日期: 2021-12-10
- 修回日期: 2021-11-10
- 网络出版日期: 2021-12-10
- 刊出日期: 2023-02-01

COMPRESSIVE PERFORMANCE STUDY OF GROUT-FILLED GFRP TUBE REPAIRING CORRODED JOINTS

CHANG Hong-fei^{1, 2
,},
GAO Yu-hang^1
,,
ZUO Wen-kang^{1, 3
, ,},
LI Zhao-wei^1
,,
YAN Xiao-yu^1
,

1.
JiangSu Key Laboratory of Environmental Impact and Structural Safety in Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China
2.
State key Laboratory of Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China
3.
School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

摘要

摘要: 圆钢管焊接节点应用广泛，长期服役后的腐蚀退化问题严重影响其安全性和剩余寿命。为研究GFRP管-灌浆料修复锈蚀钢管节点的效果，对6组未锈蚀、锈蚀未修复和GFRP管-灌浆料修复的锈蚀圆钢管T形节点开展了支管轴压力静载试验。试验结果表明：主管锈蚀导致的约10%重量损失会使节点承载力降低近20%；GFRP管-灌浆料有效地约束了锈蚀主管的侧向外凸变形，使节点的控制破坏模式由主管塑性化转变为主管冲剪，从而使锈蚀节点的受压承载力和初始刚度分别提升约100%和50%，且均高于未锈蚀的对比试件。基于验证的精细化有限元模型，进一步参数分析表明，支主管直径比、GFRP管厚度以及修复主管截面空心率是影响修复节点受压性能的关键参数，主管修复长度和灌浆料强度的影响较小；优化修复构造，可使主管重量损失28%的锈蚀节点承载力提升至锈蚀前的1.5倍以上。最后，基于修复节点承载力达到1.2倍未锈节点的目标，提出了适用于不同节点锈蚀率的修复建议，可为长期服役后锈蚀钢管结构的修复与性能提升提供参考。
- 圆钢管节点 /
- 锈蚀 /
- GFRP管 /
- 灌浆 /
- 试验研究 /
- 有限元分析
Abstract: Steel welded circular hollow section (CHS) joints are widely adopted, and the corrosion induced degradation threaten the safety and reduce the residual life of them after long-term service. To study the performance of grout-filled GFRP tube repairing corroded circular hollow section (CHS) T-joints, a total of six specimens, including uncorroded, corroded unrepaired and grout-filled GFRP tube repaired CHS T-joints were tested under brace axial compressive loading. The experimental results show that the corroded joints with around 10% chord weight loss ratio may lead to about 20% reduction of the ultimate strength. The grout-filled GFRP tube repairing is effective to prevent the ovalization of the chord, by which the joint failure mode changed from chord plasticization into chord punching shear. The ultimate strength and initial stiffness of the repaired chord corroded joints are enhanced by 100% and 50%, respectively, which are higher than those of the corresponding uncorroded ones. Based on the verified finite element models, further parametric analyses indicate that the diameter ratio of the brace to the chord, the thickness of the GFRP tube and the section hollow ratio of the repaired chord are critical parameters that determine the repairing effect. By contrast, the length of the repairing cover and the strength of the grouting layer are found to be less influential. By optimizing the configuration of the grout-filled GFRP tube repairing, the ultimate strength of the corroded joint with 28% chord weight loss ratio can be enhanced by more than 1.5 times to its corresponding uncorroded one. Finally, suggestions are proposed for the repairing of joints with different corrosion ratios, to achieve a 20% ultimate strength enhancement than uncorroded joints after repairing. The current study can provide a reference for both repairing and improving performance of corroded steel tubular joints after long-term service.
- CHS joint /
- corrosion /
- GFRP tube /
- grout filled /
- experimental investigation /
- finite element analysis

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图 1 节点形式

Figure 1. Joint details

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图 2 试验装置

Figure 2. Experimental setup

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图 3 典型破坏模式

注：EX表示实验结果；FE表示模拟结果

Figure 3. Typical failure modes

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图 4 荷载-变形曲线

Figure 4. Load-deformation curves

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图 5 有限元模型

注：f_y为钢材屈服强度；ԑ_y为钢材屈服应变；f_u为钢材极限强度, ԑ_u为钢材极限应变；E_s为钢材弹性模量；E_c为灌浆料弹性模量；ε_c0和f_c分别为灌浆料受压峰值应变和应力；ε_t0和f_t分别为灌浆料受拉峰值应变和应力；ε_c,e1和ε_c,in分别为灌浆料受压弹性和非弹性应变

Figure 5. FE models

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图 6 支主管直径比与主管重量损失率的影响

注：UU为未锈蚀节点；UC为锈蚀未修复节点；GC为GFRP管-灌浆料修复锈蚀节点

Figure 6. Influence of the brace to chord diameter ratio and the chord weight loss ratio

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图 7 GFRP外管厚度的影响

Figure 7. Influence of the thickness of GFRP tube

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图 8 修复主管截面空心率的影响

Figure 8. Influence of the repaired chord section hollow ratio

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图 9 灌浆料夹层强度的影响

Figure 9. Influence of thickness of grout sandwich

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图 10 修复长度的影响

Figure 10. Influence of repaired length

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表 1 试件信息

Table 1. Details of specimens

试件	d₀/mm	t₀/mm	L₀/mm	d₁/mm	t₁/mm	L₁/mm	d₂/mm	t₂/mm	L₂/mm	Δ/(%)	β	2γ
UU0.5	150.00	6.00	750.00	75.00	5.00	325.00	−	−	750.00	0.0	0.5	25.00
UC0.5	148.84	5.42		75.00			−	−		10.0	0.5	27.46
GC0.5	148.70	5.35		75.00			200.00	5.00		11.2	0.5	27.79
UU0.8	150.00	6.00		120.00			−	−		0.0	0.8	25.00
UC0.8	148.72	5.36		120.00			−	−		11.1	0.8	27.75
GC0.8	148.72	5.36		120.00			200.00	5.00		11.1	0.8	27.75
注：试件标签“UU”为未锈蚀节点；“UC”为锈蚀未修复节点；“GC”为GFRP管-灌浆料修复锈蚀节点；“0.5”和“0.8”分别为支主管直径比为0.5和0.8的节点；无量纲参数Δ表示根据实测平均厚度算得的主管重量损失率；β为支主管直径比；2γ为主管径厚比。

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表 2 极限承载力与初始刚度

Table 2. Ultimate strength and initial stiffness

试件	P_{r, EX}/kN	K/(kN/mm)	P_{r, FE}/kN	P_{r, EX}/P_{r, FE}
UU0.5	155	38.5	162	0.957
UC0.5	129	32.8	141	0.915
GC0.5	265	49.8	260	1.019
UU0.8	234	58.9	217	1.078
UC0.8	190	50.0	184	1.033
GC0.8	403	69.7	391	1.031
注：P_{r, EX}和P_{r, FE}分别为实测和有限元模拟的节点极限承载力；K为节点实测初始刚度。

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表 3 数值模型信息

Table 3. Detail of numerical models

分组	类型	β	Δ/(%)	τ	φ	f_cu	λ	N_FE
G1	UU	0.4	0	−				77.0
	UC	0.4	14	−				60.6
	UC	0.4	28	−				45.9
	UU	0.6	0	−				110.0
	UC	0.6	14	−				87.5
	UC	0.6	28	−				66.9
	UU	0.8	0	−				145.9
	UC	0.8	14	−				115.7
	UC	0.8	28	−				88.0
	GC	0.4	14	1.0	0.750	80	3	116.4
	GC	0.4	28	1.0	0.750	80	3	100.9
	GC	0.6	14	1.0	0.750	80	3	175.3
	GC	0.6	28	1.0	0.750	80	3	156.7
	GC	0.8	14	1.0	0.750	80	3	235.9
	GC	0.8	28	1.0	0.750	80	3	212.0
G2	GC	0.4	14	0.2	0.750	80	3	91.6
	GC	0.4	14	0.6	0.750	80	3	106.4
	GC	0.4	14	1.4	0.750	80	3	119.5
	GC	0.4	28	0.2	0.750	80	3	77.6
G2	GC	0.4	28	0.6	0.750	80	3	93.7
	GC	0.4	28	1.4	0.750	80	3	105.0
	GC	0.6	14	0.2	0.750	80	3	126.1
	GC	0.6	14	0.6	0.750	80	3	157.1
	GC	0.6	14	1.4	0.750	80	3	180.7
	GC	0.6	28	0.2	0.750	80	3	109.0
	GC	0.6	28	0.6	0.750	80	3	139.2
	GC	0.6	28	1.4	0.750	80	3	162.3
	GC	0.8	14	0.2	0.750	80	3	158.4
	GC	0.8	14	0.6	0.750	80	3	202.2
	GC	0.8	14	1.4	0.750	80	3	250.7
	GC	0.8	28	0.2	0.750	80	3	139.1
	GC	0.8	28	0.6	0.750	80	3	184.6
	GC	0.8	28	1.4	0.750	80	3	231.0
G3	GC	0.4	14	1.0	0.833	80	3	105.0
	GC	0.4	14	1.0	0.833	80	3	118.3
	GC	0.4	28	1.0	0.667	80	3	91.2
	GC	0.4	28	1.0	0.667	80	3	101.7
	GC	0.6	14	1.0	0.833	80	3	152.5
	GC	0.6	14	1.0	0.833	80	3	180.1
	GC	0.6	28	1.0	0.667	80	3	138.0
	GC	0.6	28	1.0	0.667	80	3	160.6
	GC	0.8	14	1.0	0.833	80	3	193.2
	GC	0.8	14	1.0	0.833	80	3	250.2
	GC	0.8	28	1.0	0.667	80	3	177.5
	GC	0.8	28	1.0	0.667	80	3	230.0
G4	GC	0.4	14	1.0	0.750	40	3	111.3
	GC	0.4	14	1.0	0.750	120	3	118.3
	GC	0.4	28	1.0	0.750	40	3	96.8
	GC	0.4	28	1.0	0.750	120	3	102.5
	GC	0.6	14	1.0	0.750	40	3	161.3
	GC	0.6	14	1.0	0.750	120	3	178.0
	GC	0.6	28	1.0	0.750	40	3	144.9
	GC	0.6	28	1.0	0.750	120	3	158.2
	GC	0.8	14	1.0	0.750	40	3	205.7
	GC	0.8	14	1.0	0.750	120	3	242.9
	GC	0.8	28	1.0	0.750	40	3	190.8
	GC	0.8	28	1.0	0.750	120	3	221.6
G5	GC	0.4	14	1.0	0.750	80	2	110.7
	GC	0.4	14	1.0	0.750	80	4	119.2
	GC	0.4	28	1.0	0.750	80	2	95.3
	GC	0.4	28	1.0	0.750	80	4	104.5
	GC	0.6	14	1.0	0.750	80	2	157.0
	GC	0.6	14	1.0	0.750	80	4	180.0
	GC	0.6	28	1.0	0.750	80	2	141.4
	GC	0.6	28	1.0	0.750	80	4	160.9
	GC	0.8	14	1.0	0.750	80	2	190.5
	GC	0.8	14	1.0	0.750	80	4	244.6
	GC	0.8	28	1.0	0.750	80	2	175.4
	GC	0.8	28	1.0	0.750	80	4	226.1
注：β为支主管直径比，β=d₁/d₀，d₀为主管直径，d₁为支管直径；Δ为主管锈蚀率；τ为GFRP外管与未锈蚀主管厚度比，τ=t₂/t_{0, UU}，t_{0, UU}为未锈蚀主管厚度，t₂为GFRP管厚度；φ为修复主管截面空心率，为主管外径与GFRP管内径之比，φ=d₀/(d₂−2t₂)，d₂为GFRP管外径；f_cu/MPa为灌浆料立方体抗压强度；λ为修复长度与主管外径之比，λ=L₂/d₀，L₂为GFRP管长度；N_FE/kN为模拟所得的极限承载力。

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参考文献(29)

[1]	陈以一, 王伟, 周锋. 钢管结构——新需求驱动的形式拓展和性能提升[J]. 建筑结构学报, 2019, 40(3): 1 − 20. CHEN Yiyi, WANG Wei, ZHOU Feng. Steel tubular structures: Configuration innovation and performance improvement driven by new requirements [J]. Journal of Building Structures, 2019, 40(3): 1 − 20. (in Chinese)
[2]	聂建国. 钢-混凝土组合结构在海洋工程中的应用研究(英文)[J]. 钢结构(中英文), 2020, 35(1): 20 − 33. NIE Jianguo. Application of steel-concrete composite structure in ocean engineering [J]. Steel Construction, 2020, 35(1): 20 − 33. (in Chinese)
[3]	CHANG H F, ZUO W K, XIA J W, et al. Sensitivity analysis of geometrical design parameters on the compressive strength of the vertical inner-plate reinforced square hollow section t-joints: A finite element study [J]. Engineering Structures, 2020, 208: 110308. doi: 10.1016/j.engstruct.2020.110308
[4]	潘毅, 仵振, 周祎, 等. 高强钢焊接箱形柱受力性能研究: (Ⅰ)残余应力统一分布模型 [J/OL]. 建筑结构学报, https://doi.org/10.14006/j.jzjgxb.2020.0514. PAN Yi, WU Zhen, ZHOU Yi, et al. Research on mechanical properties of high strength steel welded box columns: (Ⅰ) Unified model of residual stress [J/OL]. Journal of Building Structures, https://doi.org/10.14006/j.jzjgxb.2020.0514. (in Chinese)
[5]	赵中伟, 吴刚. 锈蚀焊接空心球节点随机抗压承载力研究[J]. 工程力学, 2021, 38(5): 219 − 228, 238. doi: 10.6052/j.issn.1000-4750.2020.07.0472 ZHAO Zhongwei, WU Gang. Random compression capacity of corroded WHSJS [J]. Engineering Mechanics, 2021, 38(5): 219 − 228, 238. (in Chinese) doi: 10.6052/j.issn.1000-4750.2020.07.0472
[6]	吴智深, 汪昕, 史健喆. 玄武岩纤维复合材料性能提升及其新型结构[J]. 工程力学, 2020, 37(5): 1 − 14. doi: 10.6052/j.issn.1000-4750.2019.07.ST10 WU Zhishen, WANG Xin, SHI Jianzhe. Advancement of basalt fiber-reinforced polymers (BFRPs) and the novel structures reinforced with BFRPs [J]. Engineering Mechanics, 2020, 37(5): 1 − 14. (in Chinese) doi: 10.6052/j.issn.1000-4750.2019.07.ST10
[7]	王宇航, 王雨嫣, 胡少伟. 海洋结构CFRP环向约束钢管混凝土柱在压弯扭荷载下的力学性能研究[J]. 工程力学, 2019, 36(8): 96 − 105. doi: 10.6052/j.issn.1000-4750.2018.07.0377 WANG Yuhang, WANG Yuyan, HU Shaowei. Study on the mechanical properties of CFRP circumferentially confined concrete filled steel tube column of marine structure under compression-bending-torsion combined load [J]. Engineering Mechanics, 2019, 36(8): 96 − 105. (in Chinese) doi: 10.6052/j.issn.1000-4750.2018.07.0377
[8]	叶列平, 冯鹏. FRP在工程结构中的应用与发展[J]. 土木工程学报, 2006, 39(3): 24 − 36. doi: 10.3321/j.issn:1000-131X.2006.03.004 YE Lieping, FENG Peng. Applications and development of fiber-reinforced polymer in engineering structures [J]. China Civil Engineering Journal, 2006, 39(3): 24 − 36. (in Chinese) doi: 10.3321/j.issn:1000-131X.2006.03.004
[9]	ZHAO X L, ZHANG L. State-of-the-art review on frp strengthened steel structures [J]. Engineering Structures, 2007, 29(8): 1808 − 1823. doi: 10.1016/j.engstruct.2006.10.006
[10]	FU Y G, TONG L W, HE L, et al. Experimental and numerical investigation on behavior of CFRP-strengthened circular hollow section gap K-joints [J]. Thin-Walled Structures, 2016, 102: 80 − 97. doi: 10.1016/j.tws.2016.01.020
[11]	XU G W, TONG L W, ZHAO X L, et al. Numerical analysis and formulae for SCF reduction coefficients of CFRP-strengthened CHS gap K-joints [J]. Engineering Structures, 2020, 210: 110369. doi: 10.1016/j.engstruct.2020.110369
[12]	TENG J G, YU T, WONG Y L, et al. Hybrid FRP-concrete-steel tubular columns: Concept and behavior [J]. Construction and Building Materials, 2007, 21(4): 846 − 854. doi: 10.1016/j.conbuildmat.2006.06.017
[13]	YU T, TENG J G, LAM E S, et al. Flexural behavior of hybrid FRP-concrete-steel double-skin tubular members [J]. Journal of Composites for Construction, 2006, 10(5): 443 − 452. doi: 10.1061/(ASCE)1090-0268(2006)10:5(443)
[14]	ZHANG B, YU T, TENG J G. Behavior and modelling of FRP-concrete-steel hybrid double-skin tubular columns under repeated unloading/reloading cycles [J]. Composite Structures, 2021, 258: 113393. doi: 10.1016/j.compstruct.2020.113393
[15]	ZENG L, LI L, XIAO P, et al. Experimental study of seismic performance of full-scale basalt FRP-recycled aggregate concrete-steel tubular columns [J]. Thin-Walled Structures, 2020, 151: 106185. doi: 10.1016/j.tws.2019.106185
[16]	DE WAAL L, JIANG S, TORRES J, et al. Design and construction of a hybrid double-skin tubular arch bridge [C]. 9th International Conference on Fibre-Reinforced Polymer (FRP) Composites in Civil Engineering (CICE), PARIS: 2018, 7: 17 − 19.
[17]	左文康, 常鸿飞, 李照伟, 等. GFRP 管夹层灌浆修复锈蚀圆钢管 T 形节点受压性能研究 [J/OL]. 建筑结构学报, https://doi.org/10.14006/j.jzjgxb.2021.0013. ZUO Wenkang, CHANG Hongfei, LI Zhaowei , et al. Investigation on compressive behavior of grout-filled GFRP tube repairing corroded CHS T-joint [J/OL]. Journal of Building Structures, https://doi.org/10.14006/j.jzjgxb.2021.0013. (in Chinese)
[18]	马昕煦, 陈以一. 支方主圆T形相贯节点轴压承载力计算公式[J]. 工程力学, 2017, 34(5): 163 − 170. doi: 10.6052/j.issn.1000-4750.2015.12.0965 MA Xinxu, CHEN Yiyi. Ultimate strength formulae for RHS-CHS T-joints under axial compression [J]. Engineering Mechanics, 2017, 34(5): 163 − 170. (in Chinese) doi: 10.6052/j.issn.1000-4750.2015.12.0965
[19]	HOU C, HAN L H, ZHAO X L. Concrete-filled circular steel tubes subjected to local bearing force: Experiments [J]. Journal of Constructional Steel Research, 2013, 83: 90 − 104. doi: 10.1016/j.jcsr.2013.01.008
[20]	CHOO Y S, VAN DER VEGTE G J, ZETTLEMOYER N, et al. Static strength of T-joints reinforced with doubler or collar plates. I: Experimental investigations [J]. Journal of Structural Engineering, 2005, 131(1): 119 − 128. doi: 10.1061/(ASCE)0733-9445(2005)131:1(119)
[21]	常鸿飞, 左文康, 任腾龙, 等. 表面焊板加强方钢管T形节点的受压性能[J]. 华南理工大学学报(自然科学版), 2019, 47(11): 113 − 121. CHANG Hongfei, ZUO Wenkang, REN Tenglong, et al. Compressive behavior of plate-reinforced square hollow section T-joints [J]. Journal of South China University of Technology (Natural Science Edition), 2019, 47(11): 113 − 121. (in Chinese)
[22]	常鸿飞, 李照伟, 钱玉龙, 等. 方钢管柱-H型钢梁槽钢连接节点受弯性能试验研究及有限元参数分析[J]. 建筑结构学报, 2021, 42(2): 92 − 102. CHANG Hongfei, LI Zhaowei, QIAN Yulong, et al. Experimental and parametric study on flexural performance of transverse reverse channel connections between square hollow section column and H-beam [J]. Journal of Building Structures, 2021, 42(2): 92 − 102. (in Chinese)
[23]	CHANG H F, ZUO W K, YANG J C, et al. Compressive strength of collar plate reinforced SHS T-joints: Effect of geometrical parameters and chord stress ratio [J]. Journal of Constructional Steel Research, 2020, 174: 106278.
[24]	聂建国, 王宇航. ABAQUS中混凝土本构模型用于模拟结构静力行为的比较研究[J]. 工程力学, 2013, 30(4): 59 − 67, 82. doi: 10.6052/j.issn.1000-4750.2011.07.0420 NIE Jianguo, WANG Yuhang. Comparison study of constitutive model of concrete in ABAQUS for static analysis of structures [J]. Engineering Mechanics, 2013, 30(4): 59 − 67, 82. (in Chinese) doi: 10.6052/j.issn.1000-4750.2011.07.0420
[25]	HASHIN Z. Failure criteria for unidirectional fiber composites [J]. Journal of Applied Mechanics, 1980, 47(2): 329 − 334.
[26]	王庆凡, 曲慧, 李伟, 等. 内置加劲环K型管节点抗冲击性能研究[J]. 工程力学, 2022, 39(5): 133 − 144. doi: 10.6052/j.issn.1000-4750.2021.02.0151 WANG Qingfan, QU Hui, LI Wei, et al. Study on impact performance of K-type tubular joints with stiffening inner rings [J]. Engineering Mechanics, 2022, 39(5): 133 − 144. (in Chinese) doi: 10.6052/j.issn.1000-4750.2021.02.0151
[27]	CHANG H F, XIA J W, GUO Z, et al. Experimental study on the axial compressive strength of vertical inner plate reinforced square hollow section T-joints [J]. Engineering Mechanics, 2018, 172: 131 − 140.
[28]	HUANG F H, CHENG B, DUAN Y H, et al. Stress concentrations and fatigue behavior of bird-beak SHS overlap K-joints subjected to brace in-plane force [J]. Thin-Walled Structures, 2021, 161: 107446. doi: 10.1016/j.tws.2021.107446
[29]	HUANG F H, CHENG B, LI C, et al. Fatigue behavior of bird-beak SHS X-joints under cyclic brace axial forces [J]. Journal of Constructional Steel Research, 2020, 169: 106021. doi: 10.1016/j.jcsr.2020.106021