﻿ 矩形钢管偏心相贯节点的平面外抗弯刚度
«上一篇
 文章快速检索 高级检索

 哈尔滨工程大学学报  2019, Vol. 40 Issue (6): 1122-1127, 1133  DOI: 10.11990/jheu.201802020 0

### 引用本文

ZHAO Bida, JIANG Wenlan, KE Ke, et al. Out-of-plane flexural rigidity of unstiffened eccentric rectangular hollow section joints[J]. Journal of Harbin Engineering University, 2019, 40(6), 1122-1127, 1133. DOI: 10.11990/jheu.201802020.

### 文章历史

1. 浙江工业大学 建筑工程学院, 浙江 杭州 310014;
2. 湖南大学 土木工程学院, 湖南 长沙 410082;
3. 西南交通大学 土木工程学院, 四川 成都 610031

Out-of-plane flexural rigidity of unstiffened eccentric rectangular hollow section joints
ZHAO Bida 1, JIANG Wenlan 1, KE Ke 2, LIU Chengqing 3
1. College of Civil Engineering and Architecture, Zhejiang University of Technology, Hangzhou 310014, China;
2. College of Civil Engineering, Hu'nan University, Changsha 410082, China;
3. School of Civil Engineering, Southwest JiaoTong University, Chengdu 610031, China
Abstract: This work applied a theoretical model method combined with numerical analysis to establish a practical parameterized calculation formula for the out-of-plane flexural rigidity of unstiffened eccentric cross-type rectangular hollow section (UECRHS) joints. A three-beam model for calculating the elastic out-of-plane flexural rigidity of UECRHS joints was established on the basis of a yield line model and the connection deformation characteristic. Then, the theoretical formula for rigidity was established and corrected in accordance with the parametric analysis results from finite element (FE) analysis. A practical parameterized calculation formula for the out-of-plane flexural rigidity of UECRHS joints was obtained through multivariable nonlinear regression analysis. Results showed that rigidity was directly proportional to the cube of chord thickness, was linearly related to the brace width-to-chord depth ratio, and had a nearly exponential function relationship with the brace-to-chord depth ratio. Moreover, the relative errors between the out-of-plane flexural rigidity values obtained by the formula and FE results were mainly less than 10%.
Keywords: rectangular hollow section(RHS)    unstiffened eccentric tubular joint    out-of-plane flexural rigidity    yield line model    three-beam model    regression analysis    parameterization calculation formula of joint rigidity    finite element analysis

1 节点的构造与有限元模型

 Download: 图 1 十字形矩形钢管偏心相贯节点构造及其受力简图 Fig. 1 Eccentric RHS cross-type joints and its force diagram

 Download: 图 3 节点的平面外弯矩-转角曲线(Mo-ψ曲线) Fig. 3 Out-of-plane bending moment-rotation curves of the joints

 Download: 图 4 试验与有限元所得节点平面外弯矩作用下的局部变形 Fig. 4 Local deformation for Eccentric RHS cross-type joints under out-of-plane moment from test and FEA result
2 节点平面外抗弯刚度的理论模型

 Download: 图 5 平面外弯矩作用下的节点局部变形区域分类 Fig. 5 Regions classification of the joint local deformation under out-of-plane bending moment
 Download: 图 6 节点平面外抗弯刚度计算的3杆系模型 Fig. 6 Three-beam model for rigidity computation of eccentric RHS cross-type joint under out-of-plane moment

 $\alpha = \arctan \sqrt {(1 - \beta )/\beta }$ (1)

 $\begin{array}{l} {K_{{\rm{oe}}}} = {M_{\rm{o}}}/\psi = F(h - t)/(\Delta /h) \approx F{h^2}/\Delta = \\ E{T^3}\left[ {\frac{{{\beta _1}{\beta ^2}}}{{3{{(1 - \beta )}^3}}} + {{\left( {\frac{\beta }{{1 - \beta }}} \right)}^{2.5}} + } \right.\\ \frac{{2\lambda \beta }}{{(1 - \beta )\left( {1 + 6\lambda \sqrt {\beta - {\beta ^2}} } \right)}}] \end{array}$ (2)
3 节点平面外抗弯刚度参数化计算式 3.1 节点平面外抗弯刚度的影响因素分析

ββ1μγτT(意义见图 1)构成确定十字形矩形钢管偏心相贯节点的几何参数，这些参数均有可能影响节点平面外抗弯刚度Koe。理论式(2)反映了KoeET3成正比、与β1呈线性关系，亦给出了Koeβ之间的函数形式，但无法反映参数γμτ的影响。以有限元为手段进行参数分析，研究各参数对Koe的影响。参数化分析的节点有限元模型类同第1节的FE3模型，但删除连接头等附加装置，主管两端施加固定约束，支管端的集中力改为集中弯矩，模型中主管长度、带槽口的支管总长度分别为10H、8h+B，钢管弹性模量E为206 GPa。

 Download: 图 7 参数T、μ、γ、τ、β1、β对节点平面外抗弯刚度Koe的影响 Fig. 7 Effect of parameters T, μ, γ, τ, β1 and β on Koe

3.2 节点平面外抗弯刚度的参数化计算式

 ${K_{{\rm{oe}}}} = E{T^3}{\mu ^{{c_0}}}\left( {{C_1} + \frac{{{C_2}}}{\gamma }} \right)\left( {\frac{{{\beta _1}{\beta ^2}}}{{3{{(1 - \beta )}^3}}} + {{\rm{e}}^{{C_3} + {C_4}\beta + {C_5}{\beta ^2}}}} \right)$ (3)

 ${K_{\rm{i}}} = E{T^3}{\mu ^{0.61}}\left( {0.29 - \frac{{0.31}}{\gamma }} \right)\left( {\frac{{{\beta _1}{\beta ^2}}}{{3{{(1 - \beta )}^3}}} + {{\rm{e}}^{1.31 - 0.19\beta + 4.11{\beta ^2}}}} \right)$ (4)

 Download: 图 8 式(4)计算值与有限元结果的误差 Fig. 8 Error of stiffness values between FEA and Eq (4)

4 结论

1) 试验和有限元结果表明，节点域在平面外弯矩作用下的局部变形大致分为近似刚体转动区域和抵抗支管传来力的支撑区域，支撑区域可进一步简化为三根梁。

2) 通过理论模型和数值分析表明，节点平面外抗弯刚度与主管壁厚T的三次方成正比、与支管截面宽度与主管截面高度之比β1呈线性关系、与主管截面高厚比的倒数γ-1呈线性关系、与主管截面高宽比μ呈幂函数关系、与支主管截面高度比β近似指数函数关系，

3) 节点抗弯刚度受支主管壁厚比τ的影响小、但受的β影响大，且参数ββ1对节点抗弯刚度存在相互影响效应，

4) 试验和有限元结果验证了节点平面外抗弯刚度参数化计算式的合理性。

 [1] OCHI K. Rotational stiffness of rectangular tubular joints-flexural rigidity equation and classification of unstiffened connections[C]//Proceedings of the 4th Pacific Structural Steel Conference. New York, 1995: 65-72. (0) [2] SILVA L A P, NEVES L F N, GOMES F C T. Rotational stiffness of rectangular hollow sections composite joint[J]. Journal of structural engineering, 2003, 129(4): 487-494. DOI:10.1061/(ASCE)0733-9445(2003)129:4(487) (0) [3] WANG Jingfeng, LI Guoqiang. A practical design method for semi-rigid composite frames under vertical loads[J]. Journal of constructional steel research, 2008, 64(2): 176-189. DOI:10.1016/j.jcsr.2007.05.005 (0) [4] 范峰, 曹正罡, 崔美艳. 半刚性节点单层球面网壳的弹塑性稳定性分析[J]. 哈尔滨工业大学学报, 2009, 41(4): 1-6. FAN Feng, CAO Zhenggang, CUI Meiyan. Elasto-plastic stability of semi-rigidity joint single-layer reticulated domes[J]. Journal of Harbin Institute of Technology, 2009, 41(4): 1-6. DOI:10.3321/j.issn:0367-6234.2009.04.001 (0) [5] MA Huihuan, FAN Feng, WEN Peng, et al. Experimental and numerical studies on a single-layer cylindrical reticulated shell with semi-rigid joints[J]. Thin-walled structures, 2015, 86: 1-9. DOI:10.1016/j.tws.2014.08.006 (0) [6] JIA L J, CHEN Y Y. Elastic axial rigidity formula for multiplanar CHS X-joint and its effect on performance of single-layered ribbed domes[C]//Proceedings of the 13th International Symposium on Tubular Structures. Hong Kong, China, 2010: 85-93. (0) [7] 武振宇, 谭慧光, 张耀春. 不等宽T型方钢管节点的刚度计算[J]. 哈尔滨建筑大学学报, 2002, 35(5): 13-16, 27. WU Zhenyu, TAN Huiguang, ZHANG Yaochun. Stiffness of stepped T-type RHS joints subjected to axial loading[J]. Journal of Harbin University of Civil Engineering and Architecture, 2002, 35(5): 13-16, 27. (0) [8] 梁战场.直接焊接K型间隙矩形管节点轴向刚度研究[D].哈尔滨: 哈尔滨工业大学, 2008. LIANG Zhanchang. Research on axial stiffness of directly welded k-type gapped RHS-Joints[D]. Harbin: Harbin Institute of Technology, 2008. http://cdmd.cnki.com.cn/Article/CDMD-10213-2009291251.htm (0) [9] AHMADI H, NEJAD A Z. Local joint flexibility of two-planar tubular DK-joints in OWTs subjected to axial loading:parametric study of geometrical effects and design formulation[J]. Ocean engineering, 2017, 136: 1-10. DOI:10.1016/j.oceaneng.2017.03.011 (0) [10] 赵必大, 刘成清, 章圣冶, 等. Y型圆钢管相贯节点轴向刚度计算模型[J]. 西南交通大学学报, 2015, 50(5): 872-878. ZHAO Bida, LIU Chengqing, ZHANG Shengye, et al. Calculation model for axial rigidity of CHS Y-type joints[J]. Journal of Southwest JiaoTong University, 2015, 50(5): 872-878. DOI:10.3969/j.issn.0258-2724.2015.05.016 (0) [11] 刘成清, 倪向勇, 赵世春. 高层斜交网格结构斜交柱节点抗震性能研究[J]. 铁道科学与工程学报, 2015, 12(3): 600-608. LIU Chengqing, NI Xiangyong, ZHAO Shichun. Research on seismic performance of the joint in high-rise non- perpendicular grid structure[J]. Journal of railway science and engineering, 2015, 12(3): 600-608. DOI:10.3969/j.issn.1672-7029.2015.03.023 (0) [12] 赵必大, 刘成清, 余丛迪, 等. 圆钢管-横向板相贯连接节点轴向刚度研究[J]. 西南交通大学学报, 2017, 52(5): 977-984. ZHAO Bida, LIU Chengqing, YU Congdi, et al. Axial rigidity of unstiffened transverse plate-to-circular hollow section (CHS) joints[J]. Journal of Southwest JiaoTong University, 2017, 52(5): 977-984. DOI:10.3969/j.issn.0258-2724.2017.05.019 (0) [13] LIU Chengqing, MA Kaiqiang. Calculation model of the lateral stiffness of high-rise diagrid tube structures based on the modular method[J]. The structural design of tall and special buildings, 2017, 26(4): e1333. DOI:10.1002/tal.1333 (0) [14] 邱国志, 赵金城. X型圆钢管相贯节点刚度试验[J]. 上海交通大学学报, 2008, 42(6): 966-970. QIU Guozhi, ZHAO Jincheng. Experimental research on rigidity of circular tubular X-joints[J]. Journal of Shanghai Jiao Tong University, 2008, 42(6): 966-970. DOI:10.3321/j.issn:1006-2467.2008.06.024 (0) [15] 赵必大, 赵滇生, 申屠倩芸, 等. 平面X形矩形钢管相贯节点平面外抗弯刚度[J]. 建筑结构学报, 2016, 37(S1): 399-405. ZHAO Bida, ZHAO Diansheng, SHENTU Qianyun, et al. Rigidity of unstiffened X-type RHS joints subjected to out-of-plane bending[J]. Journal of building structures, 2016, 37(S1): 399-405. (0) [16] 赵必大, 柯柯, 姜文澜, 等. 矩形钢管偏心相贯节点的平面外抗弯性能研究[J]. 华中科技大学学报(自然科学版), 2018, 46(7): 29-35. ZHAO Bida, KE Ke, JIANG Wenlan, et al. Research on out-plane flexural performance of unstiffened eccentric RHS joints[J]. Journal of Huazhong University of Science and Technology (nature science edition), 2018, 46(7): 29-35. (0) [17] 庄茁, 由小川, 廖剑晖, 等. 基于ABAQUS的有限元分析和应用[M]. 北京: 清华大学出版社, 2009. ZHUANG Zhuo, YOU Xiaochuan, LIAO Jianhui, et al. Finite element analysis and application based on ABAQUS[M]. Beijing: Tsinghua University Press, 2009. (0) [18] JIA L J, CHEN Y Y. Evaluation of elastic in-plane flexural rigidity of unstiffened multiplanar CHS X-joints[J]. International journal of steel structures, 2014, 14(1): 23-30. (0) [19] WARDENIER J.钢管截面的结构应用[M].张其林, 刘大康, 译.上海: 同济大学出版社, 2004. WARDENIER J. Hollow sections in structural applications[M]. ZHANG Qiling, LIU Dakang, trans. Shanghai: Tongji University Press, 2004 (0)