薄柔H形截面双向压弯钢构件极限承载力研究

杜辉波; 程欣; 张超; 陈以一

doi:10.6052/j.issn.1000-4750.2021.05.0390

薄柔H形截面双向压弯钢构件极限承载力研究

杜辉波^1,,
程欣^1, ,,
张超^1,,
陈以一^2,

1.
太原理工大学土木工程学院，山西，太原 030024
2.
上海杉达学院工程学院，上海 201209

基金项目: 国家自然科学基金面上项目(51978437)

详细信息

作者简介:
杜辉波(1998−)，男，山西运城人，硕士生，主要从事钢结构方面的研究(E-mail: duhuibo0456@link.tyut.edu.cn)

张　超(1995−)，男，山西大同人，硕士生，主要从事钢结构方面的研究(E-mail: zhangchao0350@link.tyut.edu.cn)

陈以一(1955−)，男，浙江天台人，教授，工学博士，主要从事钢结构方面的研究(E-mail: yiyichen@tongji.edu.cn)

通讯作者:
程　欣(1986−)，女，江西景德镇人，教授，博士，主要从事钢结构方面的研究(E-mail: xchengtyut@126.com)

中图分类号: TU391
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出版历程
- 收稿日期: 2021-05-24
- 修回日期: 2021-08-31
- 网络出版日期: 2021-09-17
- 刊出日期: 2022-08-31

STUDY ON ULTIMATE BEARING CAPACITY OF BIAXIAL COMPRESSION-BENDING STEEL MEMBERS WITH THIN AND SLENDER H-SHAPED SECTION

1.
College of Civil Engineering, Taiyuan University of Technology, Taiyuan, Shanxi 030024, China
2.
College of Engineering, Shanghai Sanda University, Shanghai 201209, China

摘要

摘要: 为探究薄柔H形截面双向压弯构件的极限状态性能，采用ABAQUS建立了不同轴压比、腹板和翼缘宽厚比的H形截面构件在不同加载角度下的参数分析模型，分析中考虑了材料非线性、几何非线性及残余应力的影响，并基于已有试验数据验证了该模型的适用性。基于经典弹塑性稳定理论，提出了用于确定双向压弯构件极限状态的判定准则，对于塑性铰截面定义为截面出现塑性铰时达到其极限状态；对于由局部屈曲控制的薄柔截面其极限状态为屈曲起始时刻，且该准则能够准确识别出板件局部屈曲的发生。通过最小二乘法拟合得到双轴弯矩极限相关曲线，呈现出腹板和翼缘宽厚比及轴压力的复杂相关影响关系。提出了考虑材料的强化作用和板件相关作用的极限相关计算公式，能够良好地预测H形截面双向压弯构件的极限承载力，且不受截面分类的限制，具有良好的适用性。
- 极限状态判定准则 /
- H形截面 /
- 双向压弯 /
- 局部屈曲 /
- 极限相关曲线
Abstract: To investigate the ultimate behavior of H-section members with large width-thickness ratios under a combined biaxial compression-bending, the parametric analysis models of H-section members with different axial force ratios, web and flange width-thickness ratios and different loading angles were developed by ABAQUS. Material and geometric nonlinearity were considered throughout the whole analysis, and the finite element models were validated by previous laboratory test results. Based on the elastic-plastic stability theory, a criterion for determining the ultimate state of biaxial compression-bending members was proposed. For plastic-hinge sections, the ultimate state is defined as the occurrence of plastic hinge. For slender sections controlled by local buckling, the ultimate state is the initial buckling moment, with the occurrence of plate local buckling been accurately identified through the criterion. The ultimate interactive curves of biaxial bending moments were obtained by least-square method, within which complicated interactive effects of width-thickness ratios of web and flange and the axial force were noted. The ultimate interactive formula for biaxial moments considering the strain hardening effect of material and the correlation effect of plate was proposed. Not limited by section classification, the proposed method is proved to have good applicability and accuracy.
- ultimate state criterion /
- H-section /
- combined biaxial bending and compression /
- local buckling /
- ultimate interactive curve

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图 1 截面分类方法及设计准则

注：M_pc为全截面塑性弯矩；M_ppc为部分塑性弯矩；M_ec为边缘屈服弯矩；M_u为极限抗弯承载力；f_y为屈服应力

Figure 1. Section classification method and design criterion

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图 2 悬臂构件等效原理

Figure 2. Equivalence principle of cantilever member

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图 3 受力情况及变形特点

Figure 3. Force condition and deformation features

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图 4 钢材本构模型

Figure 4. Constitutive model of structural steel

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图 5 残余应力分布及截面参数定义

Figure 5. Residual stress distribution and definition of cross-section dimensions

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图 6 网格划分与边界条件

Figure 6. Finite element meshing and boundary conditions

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图 7 加载方式

Figure 7. Loading condition

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图 8 典型试件有限元破坏模态与试验对比

Figure 8. Comparison of failure modes between finite element and test of typical specimens

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图 9 参数分析中的加载方向角

Figure 9. Loading direction angle in parametric study

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图 10 试件B-0.2-70-21-5的抗弯承载力弯矩分量发展

Figure 10. Development of moment components of B-0.2-70-21-5

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11 典型模型双向弯矩发展与极限状态

注：① σ_z,1和σ_z,5分别为有限元壳单元在上下积分面的z向应力值，拉应力为正值，压应力为负值，当σ_z,1和σ_z,5开始分岔时，表征了板件屈曲的发生；② u_e为屈服合位移，表征柱底截面受压边缘进入塑性时柱顶施加的合位移： ${u_{\text{e}}} = \dfrac{{2(1 - n){L^2}{f_{\text{y}}}}}{{3(b\cos \alpha + h\sin \alpha )E}}$ ，u为柱顶的加载合位移。

11. Development of moments about two axes and ultimate state of typical models

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图 12 典型模型双向弯矩相关关系及极限相关曲线

Figure 12. Correlation between biaxial bending moments and ultimate interactive curves of typical models

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图 13 不同轴压比下的极限相关曲线

Figure 13. Interactive curves under different axial force ratios

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图 14 现行规范与本文提出公式

Figure 14. Formulas in current codes and this paper

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15 本文提出公式的试验^[21]评价结果

15. Evaluation of the proposed formula using the test results^[21]

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16 式(6)与EC3和有限元比较结果

16. Comparison between formula (6), EC3 and FE results

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表 1 有限元结果与试验结果^[21]比较

Table 1 Comparison between finite element results and available experimental results^[21]

试件编号	r_w	r_f	M_xmax,test/ (kN·m)	M_xmax,FEA/ (kN·m)	M_xmax,test/ M_xmax,FEA	M_ymax,test/ (kN·m)	M_ymax,FEA/ (kN·m)	M_ymax,test/ M_ymax,FEA
B-H1-0.2-15	61	35	61.9	63.5	0.975	19.0	20.2	0.941
B-H2-0.2-15	117	16	79.9	87.2	0.916	20.8	20.4	1.020
B-H3-0.2-15	118	30	54.1	60.6	0.893	13.2	13.5	0.978
B-H3-0.2-30	118	30	64.5	60.9	1.059	10.2	10.2	1.000
B-H4-0.2-15	117	21	77.8	79.8	0.975	35.7	32.7	1.092
B-H4-0.2-30	117	21	103.8	94.7	1.096	26.3	27.1	0.970
B-H5-0.2-15	100	21	74.4	61.1	1.218	35.3	35.1	1.006
B-H5-0.4-15	100	21	44.8	50.2	0.892	32.9	33.1	0.994
B-H6-0.2-15	100	16	66.3	74.2	0.894	20.8	18.5	1.124
B-H7-0.2-30	42	11	130.8	128.3	1.019	30.7	27.6	1.112
B-H7-0.4-15	42	11	69.1	73.3	0.943	41.9	38.6	1.085
平均值					0.989			1.029
标准差/(%)					9.780			6.010
注： ${r_{\rm{w}}} = {h_{\rm{w}}}/{t_{\rm{w}}}\sqrt {{f_{\rm{y}}}/235}$ ， ${r_{\rm{f}}} = {b_{\rm{f}}}/{t_{\rm{f}}}\sqrt {{f_{\rm{y}}}/235}$ ；M_xmax,test和M_ymax,test分别为试验结果的强轴和弱轴弯矩分量的峰值；M_xmax,FEA和M_ymax,FEA分别为有限元结果的强轴和弱轴弯矩分量的峰值。

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表 2 参数设置范围

Table 2 Range of parameter values

关键参数	参数值
n	0, 0.1, 0.2, 0.3, 0.4, 0.5
r_w	40, 55, 70, 85, 100, 115, 130
r_f	9, 11, 13, 15, 17, 19, 21
α/(°)	0, 5, 10, 15, 20, 25, 30, 45, 60, 75, 90

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表 3 可靠度分析结果

Table 3 Reliability analysis results

截面分类	R_u,EC3/R_u,FEM		R_u,proposed/R_u,FEM
截面分类	平均值	标准差/(%)	平均值	标准差/(%)
I和II类	0.66	10.32	1.01	4.43
III类	0.56	13.69	0.98	4.94
IV类	0.47	14.60	0.97	7.48
I~IV类	0.50	14.97	0.98	6.99

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