间隙K型节点方管桁架支杆平面外计算长度系数研究
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摘要
采用直接焊接连接的空心管桁架中,受压腹杆一般都有相当大的端部约束,一般情况下其计算长度系数μ均小于1.0。欧洲标准Eurocode3规定对直接焊接空心管桁架腹杆,计算长度系数取0.75。而我国规范并没有对此进行规定,工程中一般按铰接体系进行设计,计算长度取其几何长度,取值很保守,所以很有必要进行这方面的研究。本文利用有限元程序ANSYS对采用K型间隙节点的方钢管桁架腹杆平面外计算长度系数进行了大规模的参数分析。
首先,将桁架支杆简化为两端受弹性转动约束的轴心受压构件,根据钢结构稳定理论,建立构件平衡微分方程,推导出杆件稳定承载力公式。当杆件两端转动刚度为已知时,便可以求得支杆稳定承载力。根据欧拉公式便可以反推出支杆计算长度系数μ。
其次,建立节点有限元模型,计算出节点平面外转动刚度。考虑支弦杆宽度比β、弦杆宽厚比γ、支弦杆厚度比τ、支杆高度与弦杆宽度比η、节点间隙g、支弦杆夹角θ、整体尺寸比C等参数的影响,对节点平面外转动刚度进行大规模参数分析。通过300多个节点算例分析得出节点平面外转动刚度随节点参数的变化规律。
根据有限元计算结果,对节点平面外转动刚度进行多元回归分析,得出节点转动刚度的计算公式。将回归公式计算出来的结果与有限元计算结果进行对比,两者符合较好,回归效果良好。
根据本文推导出的弹性转动约束下压杆稳定承载力公式,结合求得的支杆两端节点转动刚度,计算出受压支杆平面外计算长度系数μ,并分析计算长度系数μ随节点几何参数的变化规律。通过多元回归分析,推导出计算长度系数的计算公式。
In HSS (Hollow Structural Sections) truss, the chords provide great restraints on the braces. So the effective length factor of braceμis less than 1.0. According to the Eurocode3, The effective length factor of brace of directly welded HSS truss is 0.75. However, the effective length factor of HSS truss is not specified in Chinese Code. In practice, HSS truss is supposed to be pinned. So it is necessary to do some research on the effective length factor of HSS truss. In this paper, a systematic parametric research on effective length factor of compression brace is carried out by ANSYS.
Firstly, the compression brace is simplified as an axial compression member with elastic rotational restraints. According to stability theory of steel structures, the equilibrium differential equation is established. From the equation, the stability formula of compression brace is obtained. Then, the effective length factor of brace is obtained by stability formula and the Euler formula when the rotational stiffness is available.
Secondly, the FE model of gapped K-joint is established. Then the out-of-plane rotational stiffness of the joint is calculated. Extensive FE analysis for out-of-plane rotational stiffness of the joint is conducted. Considering the parameters such asβ,γ,τ, g,η,θ, C, more than 300 joints are analyzed and the variation of rotational stiffness of the joint with geometrical parameters are available.
Through the multi-parameter regressive analysis, equations calculating out-of-plane rotational stiffness of the joint are acquired. The out-of-plane rotational stiffness of the joint calculated from the equations coincide with the results that are obtained by finite element analysis.
According to the stability formula of brace and the rotational stiffness of the joint, the effective length factor is calculated. The variation of effective length factor with the geometrical parameters is obtained. The equation calculating the effective length factor is acquired through multi-parameter regressive analysis.
首先,将桁架支杆简化为两端受弹性转动约束的轴心受压构件,根据钢结构稳定理论,建立构件平衡微分方程,推导出杆件稳定承载力公式。当杆件两端转动刚度为已知时,便可以求得支杆稳定承载力。根据欧拉公式便可以反推出支杆计算长度系数μ。
其次,建立节点有限元模型,计算出节点平面外转动刚度。考虑支弦杆宽度比β、弦杆宽厚比γ、支弦杆厚度比τ、支杆高度与弦杆宽度比η、节点间隙g、支弦杆夹角θ、整体尺寸比C等参数的影响,对节点平面外转动刚度进行大规模参数分析。通过300多个节点算例分析得出节点平面外转动刚度随节点参数的变化规律。
根据有限元计算结果,对节点平面外转动刚度进行多元回归分析,得出节点转动刚度的计算公式。将回归公式计算出来的结果与有限元计算结果进行对比,两者符合较好,回归效果良好。
根据本文推导出的弹性转动约束下压杆稳定承载力公式,结合求得的支杆两端节点转动刚度,计算出受压支杆平面外计算长度系数μ,并分析计算长度系数μ随节点几何参数的变化规律。通过多元回归分析,推导出计算长度系数的计算公式。
In HSS (Hollow Structural Sections) truss, the chords provide great restraints on the braces. So the effective length factor of braceμis less than 1.0. According to the Eurocode3, The effective length factor of brace of directly welded HSS truss is 0.75. However, the effective length factor of HSS truss is not specified in Chinese Code. In practice, HSS truss is supposed to be pinned. So it is necessary to do some research on the effective length factor of HSS truss. In this paper, a systematic parametric research on effective length factor of compression brace is carried out by ANSYS.
Firstly, the compression brace is simplified as an axial compression member with elastic rotational restraints. According to stability theory of steel structures, the equilibrium differential equation is established. From the equation, the stability formula of compression brace is obtained. Then, the effective length factor of brace is obtained by stability formula and the Euler formula when the rotational stiffness is available.
Secondly, the FE model of gapped K-joint is established. Then the out-of-plane rotational stiffness of the joint is calculated. Extensive FE analysis for out-of-plane rotational stiffness of the joint is conducted. Considering the parameters such asβ,γ,τ, g,η,θ, C, more than 300 joints are analyzed and the variation of rotational stiffness of the joint with geometrical parameters are available.
Through the multi-parameter regressive analysis, equations calculating out-of-plane rotational stiffness of the joint are acquired. The out-of-plane rotational stiffness of the joint calculated from the equations coincide with the results that are obtained by finite element analysis.
According to the stability formula of brace and the rotational stiffness of the joint, the effective length factor is calculated. The variation of effective length factor with the geometrical parameters is obtained. The equation calculating the effective length factor is acquired through multi-parameter regressive analysis.
引文
1 J. A. Packer, J.E. Henderson, J. J. cao(曹俊杰).空心管结构连接设计指南.科学出版社, 1997: 1~124 316~370
2 J. Wardenier著,张其林,刘大康译.钢管截面的结构应用.同济大学出版社,2004:1～66
3武振宇,张耀春.直接焊接钢管节点静力工作性能的研究现状.哈尔滨建筑大学学报. 1996,29(6):102~109
4 J.A. Packer, et al. Ultimate Strength of Gapped Joints in RHS Truss. J. Struct. Engrg., ASCE, 1982, 108(2): 411~431
5 X.L. Zhao, G.J. Hancock. Plastic Mechanism Analysis of T-Joints in RHS under Concentrated Force. Res. Report No.R644, Univ.of Sydney, 1991.
6 X.L. Zhao, G.J. Hancock. T-Joints in Rectangular Hollow Section Subject to Combined Actions. J. Struct. Engrg., 1991, 117(8): 2258~2277
7 J.A.Yura, et al. Ultimate Capacity of Circular Tubular Joints. ASCE, 1981,107(10): 1965~1984
8 R.M.Korol, et al. Finite Element Analysis of RHS T-Joints. J. Struct. Engrg., ASCE, 1982, 108(9): 2081~2098
9 Yoshiaki Kurobane. Ultimate Resistance of Unstiffened Tubular Joints. J. Struct. Engrg., ASCE, 1984, 110(2): 385~440
10 J.A. Packer. Web Ctippling of Rectangular Hollow Section. J. Struct. Engrg., ASCE, 1984, 110(10): 2357~2373
11 Dominique Bauer and Richard G. Redwood. Triangular Truss Joints Using Rectangular Tubes. J. Struct. Engrg., ASCE, 1988, 114(2): 408~424
12 W.F. Cofer, et al. Analysis of Welded Tubular Connections Using Contimuum Damage Mechanics. J. Structu. Engrg., ASCE, 1992, 118(3): 828~845
13 X.L.Zhao, and G.J. Hancock. Plastic Mechanism Analysis of T-Joints in RHS Subjected to Combined Bending and Concentruted Force. Res. Report No.R673, Univ.of Sydney,1993
14 J.C. Paul. Ultimate Resistance of Unstiffened Multiplanar Tubular TT-and KK-joints. J. Struct. Engrg., ASCE, 1994, 120(10): 2853~2870
15 M.M.K.Lee, S.R. Wilmshurst. Paramettric Study of Tubular Multiplanar KK-joints. J. Struct. Engrg., ASCE, 1996,122(8):893~904
16 M. Saidani. The Effect of Joint Eccentrieity on the Dstribution of Forces in RHS Lattice Girders. Journal of Constr. Steel RES, 1998, 47: 200~221
17 X. L. Zhao. Deformation Limit and Ultimate Strength of Welded T-joints in Cold-formed RHS Sections. Journal of Constr. steel RES, 2000,53: 149~165
18 T.C.Fung, C.K.Soh, W.M.Gho. Ultimate Capacity of Completely Overlapped Tubular Joints. I: An Experimental Investigation. Journal of Constructional Steel Research. 2001,57:855~880
19 T.C.Fung, C.K.Soh, W.M.Gho. Ultimate Capacity of Completely Overlapped Tubular Joints. II: Behavior Study. Journal of Constructional Steel Research. 2001,57:881~906
20 W.M.Gho, F.Gao. Parametric Equations for Stress Construction Factors in Completely Overlapped Tubular K (N)-jionts. Journal of constructional Steel Research. 2004,60:1761~1782
21云大真. T型管节点的拟协调元的计算.计算结构力学及其应用. Vol.6.NO.1,Feb. 1989:217~223
22张志良,沈祖炎,陈学潮.方管节点极限承载力的非线性有限元分析.土木工程学报. 1990,23(1): 12~22
23贺东哲,李少甫.管节点承载力的非线性有限元分析.工程力学. 2000,(17)4: 48~55
24刘建平,郭彦林. K型方、圆管相贯节点的极限承载力非线性有限元分析.建筑科学. 2001, 17(2): 50~53
25陈以一,陈扬骥,詹琛,林颍如,董明.圆钢管空间相贯节点的实验研究.土木工程学报. Vol.36.NO.8,Aug. 2003:24~30
26石永久,祝磊,王元清.弦杆轴向应力对TX型和XX型矩形管节点承载力的影响.空间结构. 2005,11(1):8~12
27武振宇,张耀春.直接焊接T型钢管节点性能的试验研究.钢结构. 1999,14(2):36~40
28武振宇,谭慧光,张耀春.不等宽T型方钢管节点的刚度计算.哈尔滨建筑大学学报. 2002, 35(5): 13~16
29武振宇,张耀春.轴向力作用下T型方管节点的塑性铰线分析.土木工程学报. 2002,35(4): 20~24
30武振宇,张耀春.压弯组合时等宽T型方管节点承载力计算.低温建筑技术. 2003, 5: 36~37
31武胜.直接焊接K型、N型间隙钢管节点静力工作性能的研究.哈尔滨工业大学硕士学位论文. 2002, 9~42
32张壮南.直接焊接K型、KK型间隙方钢管节点静力性能的试验研究.哈尔滨工业大学硕士学位论文. 2003, 28~79
33丁玉坤.直接焊接K型、KK型搭接方钢管节点静力性能的研究.哈尔滨工业大学硕士学位论文. 2003, 49~103
34向斌.直接焊接K型、KK型间隙方管节点静力性能研究.哈尔滨工业大学硕士学位论文. 2005,9～79
35张扬.直接焊接KT型搭接方管节点静力性能研究.哈尔滨工业大学硕士学位论文. 2006,13～97
36 Y.Furukawa, Y.Makino, Y.Kurobane. Study on Out-of-plane Rotational Stiffness of CHS Joints and Effective Column Length of Web Members in CHS Lattice Girder. Tubular Structures VIII, 1998:457~463
37 Y.Furukawa, K.Adachi, Y.Makino, Y.Kurobane. Tests on the Effective Column Length of Web Members in CHS Lattice Girder. Proceedings of the 9th(1999) International Offshore and Polar Engineering Conference. Vol.IV, 1999:71~77
38 U.Hornung, H.Saal. A Method for Calculating the Out-of-plane Buckling Length of Diagonals of Truss Girders with Hollow Sections and K-joint. J.Construct. Steel Res. 1998,Vol.46
39李海旺,肖毓恺,李铁英.焊接空心球节点钢管杆系结构杆件计算长度系数的研究.工程力学增刊. 1996,570～574
40刘鹏.方圆汇交平面钢管节点的刚度研究.同济大学硕士学位论文. 2001,5～62
41胡星岩,张晓光,杨建行,罗晓群.空间钢管桁架结构的整体稳定分析.工程力学增刊. 2001,481～485
42贺喜霞.空间相贯节点钢管桁架中杆件的计算长度.西安建筑科技大学硕士学位论文. 2003,6～50
43张春雷,何敏娟.四边形钢管塔中十字交叉斜杆的平面内计算长度.特种结构. Vol.21 .N0.1,March 2004:44~46
44彭晓丹,梁启龙,满杰.相贯节点平面钢管桁架中受压腹杆的计算长度系数研究.工业建筑. Vol.35 .N0.6,2005:76～79
45王伟,陈以一.节点半刚性钢桁架受压腹杆计算长度分析.工程力学. Vol.22 .N0.5,Oct. 2005:131～135
46苏锐.直接焊接方管桁架支杆计算长度系数研究.哈尔滨工业大学硕士学位论文. 2005:3～73
47刘娟.采用搭接节点的方管桁架支杆平面内计算长度系数研究.哈尔滨工业大学硕士学位论文. 2006:7～74
2 J. Wardenier著,张其林,刘大康译.钢管截面的结构应用.同济大学出版社,2004:1～66
3武振宇,张耀春.直接焊接钢管节点静力工作性能的研究现状.哈尔滨建筑大学学报. 1996,29(6):102~109
4 J.A. Packer, et al. Ultimate Strength of Gapped Joints in RHS Truss. J. Struct. Engrg., ASCE, 1982, 108(2): 411~431
5 X.L. Zhao, G.J. Hancock. Plastic Mechanism Analysis of T-Joints in RHS under Concentrated Force. Res. Report No.R644, Univ.of Sydney, 1991.
6 X.L. Zhao, G.J. Hancock. T-Joints in Rectangular Hollow Section Subject to Combined Actions. J. Struct. Engrg., 1991, 117(8): 2258~2277
7 J.A.Yura, et al. Ultimate Capacity of Circular Tubular Joints. ASCE, 1981,107(10): 1965~1984
8 R.M.Korol, et al. Finite Element Analysis of RHS T-Joints. J. Struct. Engrg., ASCE, 1982, 108(9): 2081~2098
9 Yoshiaki Kurobane. Ultimate Resistance of Unstiffened Tubular Joints. J. Struct. Engrg., ASCE, 1984, 110(2): 385~440
10 J.A. Packer. Web Ctippling of Rectangular Hollow Section. J. Struct. Engrg., ASCE, 1984, 110(10): 2357~2373
11 Dominique Bauer and Richard G. Redwood. Triangular Truss Joints Using Rectangular Tubes. J. Struct. Engrg., ASCE, 1988, 114(2): 408~424
12 W.F. Cofer, et al. Analysis of Welded Tubular Connections Using Contimuum Damage Mechanics. J. Structu. Engrg., ASCE, 1992, 118(3): 828~845
13 X.L.Zhao, and G.J. Hancock. Plastic Mechanism Analysis of T-Joints in RHS Subjected to Combined Bending and Concentruted Force. Res. Report No.R673, Univ.of Sydney,1993
14 J.C. Paul. Ultimate Resistance of Unstiffened Multiplanar Tubular TT-and KK-joints. J. Struct. Engrg., ASCE, 1994, 120(10): 2853~2870
15 M.M.K.Lee, S.R. Wilmshurst. Paramettric Study of Tubular Multiplanar KK-joints. J. Struct. Engrg., ASCE, 1996,122(8):893~904
16 M. Saidani. The Effect of Joint Eccentrieity on the Dstribution of Forces in RHS Lattice Girders. Journal of Constr. Steel RES, 1998, 47: 200~221
17 X. L. Zhao. Deformation Limit and Ultimate Strength of Welded T-joints in Cold-formed RHS Sections. Journal of Constr. steel RES, 2000,53: 149~165
18 T.C.Fung, C.K.Soh, W.M.Gho. Ultimate Capacity of Completely Overlapped Tubular Joints. I: An Experimental Investigation. Journal of Constructional Steel Research. 2001,57:855~880
19 T.C.Fung, C.K.Soh, W.M.Gho. Ultimate Capacity of Completely Overlapped Tubular Joints. II: Behavior Study. Journal of Constructional Steel Research. 2001,57:881~906
20 W.M.Gho, F.Gao. Parametric Equations for Stress Construction Factors in Completely Overlapped Tubular K (N)-jionts. Journal of constructional Steel Research. 2004,60:1761~1782
21云大真. T型管节点的拟协调元的计算.计算结构力学及其应用. Vol.6.NO.1,Feb. 1989:217~223
22张志良,沈祖炎,陈学潮.方管节点极限承载力的非线性有限元分析.土木工程学报. 1990,23(1): 12~22
23贺东哲,李少甫.管节点承载力的非线性有限元分析.工程力学. 2000,(17)4: 48~55
24刘建平,郭彦林. K型方、圆管相贯节点的极限承载力非线性有限元分析.建筑科学. 2001, 17(2): 50~53
25陈以一,陈扬骥,詹琛,林颍如,董明.圆钢管空间相贯节点的实验研究.土木工程学报. Vol.36.NO.8,Aug. 2003:24~30
26石永久,祝磊,王元清.弦杆轴向应力对TX型和XX型矩形管节点承载力的影响.空间结构. 2005,11(1):8~12
27武振宇,张耀春.直接焊接T型钢管节点性能的试验研究.钢结构. 1999,14(2):36~40
28武振宇,谭慧光,张耀春.不等宽T型方钢管节点的刚度计算.哈尔滨建筑大学学报. 2002, 35(5): 13~16
29武振宇,张耀春.轴向力作用下T型方管节点的塑性铰线分析.土木工程学报. 2002,35(4): 20~24
30武振宇,张耀春.压弯组合时等宽T型方管节点承载力计算.低温建筑技术. 2003, 5: 36~37
31武胜.直接焊接K型、N型间隙钢管节点静力工作性能的研究.哈尔滨工业大学硕士学位论文. 2002, 9~42
32张壮南.直接焊接K型、KK型间隙方钢管节点静力性能的试验研究.哈尔滨工业大学硕士学位论文. 2003, 28~79
33丁玉坤.直接焊接K型、KK型搭接方钢管节点静力性能的研究.哈尔滨工业大学硕士学位论文. 2003, 49~103
34向斌.直接焊接K型、KK型间隙方管节点静力性能研究.哈尔滨工业大学硕士学位论文. 2005,9～79
35张扬.直接焊接KT型搭接方管节点静力性能研究.哈尔滨工业大学硕士学位论文. 2006,13～97
36 Y.Furukawa, Y.Makino, Y.Kurobane. Study on Out-of-plane Rotational Stiffness of CHS Joints and Effective Column Length of Web Members in CHS Lattice Girder. Tubular Structures VIII, 1998:457~463
37 Y.Furukawa, K.Adachi, Y.Makino, Y.Kurobane. Tests on the Effective Column Length of Web Members in CHS Lattice Girder. Proceedings of the 9th(1999) International Offshore and Polar Engineering Conference. Vol.IV, 1999:71~77
38 U.Hornung, H.Saal. A Method for Calculating the Out-of-plane Buckling Length of Diagonals of Truss Girders with Hollow Sections and K-joint. J.Construct. Steel Res. 1998,Vol.46
39李海旺,肖毓恺,李铁英.焊接空心球节点钢管杆系结构杆件计算长度系数的研究.工程力学增刊. 1996,570～574
40刘鹏.方圆汇交平面钢管节点的刚度研究.同济大学硕士学位论文. 2001,5～62
41胡星岩,张晓光,杨建行,罗晓群.空间钢管桁架结构的整体稳定分析.工程力学增刊. 2001,481～485
42贺喜霞.空间相贯节点钢管桁架中杆件的计算长度.西安建筑科技大学硕士学位论文. 2003,6～50
43张春雷,何敏娟.四边形钢管塔中十字交叉斜杆的平面内计算长度.特种结构. Vol.21 .N0.1,March 2004:44~46
44彭晓丹,梁启龙,满杰.相贯节点平面钢管桁架中受压腹杆的计算长度系数研究.工业建筑. Vol.35 .N0.6,2005:76～79
45王伟,陈以一.节点半刚性钢桁架受压腹杆计算长度分析.工程力学. Vol.22 .N0.5,Oct. 2005:131～135
46苏锐.直接焊接方管桁架支杆计算长度系数研究.哈尔滨工业大学硕士学位论文. 2005:3～73
47刘娟.采用搭接节点的方管桁架支杆平面内计算长度系数研究.哈尔滨工业大学硕士学位论文. 2006:7～74