具有变截面臂架的格构式起重机结构计算分析方法研究
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摘要
随着工程建设发展的需要,起重机日益向着大型、高耸、轻柔化、格构式方向发展。由于高强度钢材的大量采用,提高了结构强度,却使刚度和稳定性问题日显突出。复杂桁架式结构的稳定性分析已成为当代大型起重机结构设计计算的难点。具有变截面臂架的格构式起重机之整体稳定性分析更是目前我国起重机设计分析人员所面临的难题。因此,结合起重机设计规范,寻求一种简单、实用、有效的方法极为必要。
通过对类似塔式起重机变截面臂架的悬臂格构式结构进行受力分析,引入了这类变截面悬臂结构端部侧向位移的便捷算式。在此基础上,通过位移比较的方法,得出了变截面双肢格构式构件等效为等截面实腹式构件时等效惯性矩的计算公式。并进一步延伸到四肢格构式构件等效惯性矩的计算,给出了变截面四肢格构式构件等效为等截面实腹式构件时,等效惯性矩的计算公式。
用有限单元法对不同腹杆布置形式下的变截面构件进行了稳定性分析,对等效惯性矩的计算公式进行了验证。在不改变构件长度的情况下,实现了变截面格构式结构到等截面实腹式结构的等效。
对具有变截面臂架的起重机格构式臂架整体稳定性进行了研究,利用上述等效原则将具有变截面结构的臂架等效为实腹式阶梯柱,采用精确有限元理论,列写出多级阶梯柱的组装精确刚度矩阵,由此给出了求解具有变截面结构臂架的失稳临界载荷的计算方法。
将本文所研究的等效方法应用于具有变截面臂架的格构式起重机的整体稳定性及结构变形的验算。借助通用有限元程序对FZQ1650动臂式塔机的实际全结构模型及等效模型进行了分析,算例表明,等效惯性矩法有足够的计算分析精度,可供工程设计应用。
With the demand of the engineering construction development, the development of crane is increasingly prone to large-sized, dominant-mountain and lattice. By the great deal use of the high-strength steel material, the structure strength is raised, but the problem of structural stiffness and structural stability is made to show to project. The stability analysis of complicated lattice structure becomes the crux of contemporary and large crane structure design and its calculation. The overall stability analysis of the crane’s lattice jib with main and vice-jib structure is even more difficult to technician in our country. So it’s very necessary to seek a simple, utility and effective method to solve the difficulty.
By means of internal force analyses to the cantilever lattice structure such as the tower crane which with variable cross-section boom, a simple lateral movement formula is introduced. On the basis of this, the contrast of the algorithm is used in cantilever lattice structure and cantilever solid web beam, we can get the algorithm that can be used to calculate the equivalent inertia moment of the lattice structure when it is regarded as solid web beam.
The application of finite element method in the stability analysis is studied by calculate the lattice structure’s equivalent inertia moment in the different arrangements of web member, by this way to test the accuracy of the formula. The initial moment method is improved. So we can realize the equivalent between lattice structure and solid web beam without change its geometry dimension.
The overall stability of crane’s lattice boom with variable cross-section structure is studied. Use the related equivalent principle, turn the variable cross-section boom to the solid ladder cylinder. The accurate finite element theory is studied to give the fabricated stiffness matrix, by use of this, the calculation of Euler's critical stress which with variable cross-section boom is given. The equivalent method is applied to test the crane’s overall stability and structural deformation. To analysis the boom-tower crane FZQ1650’s model between the actual structure and the equivalent structure with the finite element procedure, the result show that the studied equivalent method has enough accuracy, it can be used in actual project.
通过对类似塔式起重机变截面臂架的悬臂格构式结构进行受力分析,引入了这类变截面悬臂结构端部侧向位移的便捷算式。在此基础上,通过位移比较的方法,得出了变截面双肢格构式构件等效为等截面实腹式构件时等效惯性矩的计算公式。并进一步延伸到四肢格构式构件等效惯性矩的计算,给出了变截面四肢格构式构件等效为等截面实腹式构件时,等效惯性矩的计算公式。
用有限单元法对不同腹杆布置形式下的变截面构件进行了稳定性分析,对等效惯性矩的计算公式进行了验证。在不改变构件长度的情况下,实现了变截面格构式结构到等截面实腹式结构的等效。
对具有变截面臂架的起重机格构式臂架整体稳定性进行了研究,利用上述等效原则将具有变截面结构的臂架等效为实腹式阶梯柱,采用精确有限元理论,列写出多级阶梯柱的组装精确刚度矩阵,由此给出了求解具有变截面结构臂架的失稳临界载荷的计算方法。
将本文所研究的等效方法应用于具有变截面臂架的格构式起重机的整体稳定性及结构变形的验算。借助通用有限元程序对FZQ1650动臂式塔机的实际全结构模型及等效模型进行了分析,算例表明,等效惯性矩法有足够的计算分析精度,可供工程设计应用。
With the demand of the engineering construction development, the development of crane is increasingly prone to large-sized, dominant-mountain and lattice. By the great deal use of the high-strength steel material, the structure strength is raised, but the problem of structural stiffness and structural stability is made to show to project. The stability analysis of complicated lattice structure becomes the crux of contemporary and large crane structure design and its calculation. The overall stability analysis of the crane’s lattice jib with main and vice-jib structure is even more difficult to technician in our country. So it’s very necessary to seek a simple, utility and effective method to solve the difficulty.
By means of internal force analyses to the cantilever lattice structure such as the tower crane which with variable cross-section boom, a simple lateral movement formula is introduced. On the basis of this, the contrast of the algorithm is used in cantilever lattice structure and cantilever solid web beam, we can get the algorithm that can be used to calculate the equivalent inertia moment of the lattice structure when it is regarded as solid web beam.
The application of finite element method in the stability analysis is studied by calculate the lattice structure’s equivalent inertia moment in the different arrangements of web member, by this way to test the accuracy of the formula. The initial moment method is improved. So we can realize the equivalent between lattice structure and solid web beam without change its geometry dimension.
The overall stability of crane’s lattice boom with variable cross-section structure is studied. Use the related equivalent principle, turn the variable cross-section boom to the solid ladder cylinder. The accurate finite element theory is studied to give the fabricated stiffness matrix, by use of this, the calculation of Euler's critical stress which with variable cross-section boom is given. The equivalent method is applied to test the crane’s overall stability and structural deformation. To analysis the boom-tower crane FZQ1650’s model between the actual structure and the equivalent structure with the finite element procedure, the result show that the studied equivalent method has enough accuracy, it can be used in actual project.
引文
1顾迪民.工程起重机.第二版.中国建筑工业出版社, 1998: 257-275
2陈骥.钢结构稳定理论与设计.科学出版社, 2003: 11-24
3顾迪民.起重机械事故分析和对策.人民出版社, 2001: 210-224
4 Timoshenko SP, Gere JM. Theory of elastic stability. 2nd ed. New York: McGraw-Hill, 1961.
5 A.查杰斯.结构稳定性理论原理.唐家祥译.甘肃人民出版社, 1982: 71-103
6 Loannis G. Raftoyiannis, John Ch. Ermopoulos. Stability of Tapered and Stepped Steel Columns with Initial Imperfections. Engineering Structures. 2005, 27(8): 1248-1257
7 W.F. Chen. Structural Stability: From Theory to Practice. Engineering Structures. 2000, 22(2): 116-122
8刘光栋,罗汉泉.杆系结构稳定.人民交通出版社, 1988: 1-4
9楚中毅,陆念力,车仁炜,楚兰英.一种梁杆结构稳定性分析的精确有限元法.哈尔滨建筑大学学报, 2002, 35(4): 25-28
10李以申,陆念力,顾迪民.塔式起重机起重臂结构稳定计算的研究(三)——微分方程法求解阶梯状变截面非保向力悬臂梁构件的失稳临界力.建筑机械, 1997(1): 12-19
11李以申,陆念力,顾迪民.塔式起重机起重臂结构稳定计算的研究(一)——验算公式的使用和说明.建筑机械, 1996(12): 23-26
12张连文,郭卫军,王昊,马新敏,张忠海,陈以田,刘振.双吊点臂架整体稳定性校核段的选择.建筑机械化, 2003(2): 28-29
13李涵,塔式起重机双吊点水平臂整体稳定性分析研究.哈尔滨工业大学硕士学位论文. 2005: 29-36
14 GB 3811-83,起重机设计规范: 56-60
15 N.S. Trahair. Torsion, Bending and Buckling of Steel Beams. Engineering Structures. 1997, 19(5): 372-377
16 Lan Peng, Liu Manlan, Lu Nianli. Out-of-plane stability of a bending beam. GongchengLixue, 2005, 22: 152-155
17王佳,具有主副臂结构的起重机格构式臂架整体稳定性研究.哈尔滨工业大学硕士学位论文. 2006: 17-22
18薛渊.塔式起重机塔身刚度计算分析的高效方法.哈尔滨工业大学硕士学位论文. 2001: 25-30
19任体旺.格构式轴压构件稳定性计算及精度分析.哈尔滨工业大学硕士毕业论文. 2004: 35-52
20郑惠强.变截面悬臂构件顶端水平位移的简便计算.工程机械, 1992(7):21-23
21 O.C. Zienkiewicz, R.L. Taylor. The Finite Element Method. 5th Edi. Butterwort-Heinemann. 2000: 1-17
22 Klaus-Jürgen Bathe. Advances in Nonlinear Finite Element Analysis of Automobiles. 1997, 64(5): 881-891
23 Klaus-Jürgen Bathe. Finite Element procedures. Prentice Hall, Inc. 1996: 485-628
24蓝天,姚卓智.桅杆结构的非线形分析.中国建筑研究院结构所, 1980:2-4
25陆念力,兰朋,李良.二阶理论条件下的梁杆系统精确有限元方程及应用.哈尔滨建筑大学学报, 1998,31(4): 67-74
26陆念力,张立强,孟小平.梁杆系统精确有限元方程及其在几何非线性分析和稳定计算中的应用.建筑机械, 1996(3): 18-20
27陆念力.大位移梁杆非线性分析的一种使用方法. 1990(9):8-12
28陆念力,顾迪民.大位移杆系结构几何非线性分析与稳定性计算的有限元方法.建筑机械, 1991(10):8-12
29 S.Shimizu, M.Nakano. Strength and Behavior of the Corner Zones in Steel Rigid Frame Columns with Shifted Beams. Journal of Constructional Steel Research. 2000, 53(2): 245-263
30 Potrc I, Sraml M. On the Numerical Analysis of the Contact Problems at Crane Machanisms. Zeitschrift fur Angewandte Mathematik and Mechanik, 2000, 80(suppl2): S491-S492
31陈玮璋.起重机金属结构.人民交通出版社, 1987, 11
32 Edited by Edwin H.Gaylord Jr Charles N.Gaylord Structural Engineering Handbook. Second Edition
33王勖成.有限单元法.清华大学出版社, 2003: 55-77
34胡永飞.塔身腹杆体系探讨.建筑机械, 1992(2): 20-22
35 Mayer.G.Krafte an Raumfachwerkern Torsionsbeanspruchung Van Fachwerkturmen mit rechtechigem Querschnitt and parallelen seiten.fh.23.1973.13
36 S.P.铁摩辛柯.弹性稳定理论(第二版).科学出版社, 1965
37 Sung-Bo Kim, Moon-Young Kim. Improved formulation for spatial stability and free vibration of thin-walled tapered beams and space frames [J]. Engineering Structures. 2000, 22 (5): 446-458
38 Kiyohiro Imai, Dan M. Frangopol. Geometrically Nonlinear Finite Element Reliability Analysis of Structural Systems. Computers and Structures. 2000, 77(6): 677-691
39张质文,虞和谦,王金诺等.起重机设计手册.北京:中国铁道出版社, 1998
40李以申,陆念力,顾迪民.塔式起重机起重臂结构稳定计算的研究(二)——具有连续变化截面桁架构件的失稳临界力计算.建筑机械, 1996(12): 23-26
41李以申,陆念力,顾迪民.塔式起重机起重臂结构稳定计算的研究(四)——转角位移方程法求解构件失稳临界力.建筑机械, 1997(2): 9-13
42尹刚,冯贤桂.变截面压杆的临界压力近似计算.重庆工学院学报. 2005(11):22-24
43 Hasan ?ztürk, Mustafa Sabuncu. Stability analysis of a cantilever composite beam on elastic supports. Composites Science and Technology. 2005(65): 1982–1995
44陆念力,张立强.梁杆系统临界屈曲精确有限元判式及其应用.建筑机械化, 1996, (6): 8-10
45陆念力,兰朋,白桦.起重机箱形伸缩臂稳定性分析的精确理论解,哈尔滨建筑大学学报, 2000, 35(2): 89-93
2陈骥.钢结构稳定理论与设计.科学出版社, 2003: 11-24
3顾迪民.起重机械事故分析和对策.人民出版社, 2001: 210-224
4 Timoshenko SP, Gere JM. Theory of elastic stability. 2nd ed. New York: McGraw-Hill, 1961.
5 A.查杰斯.结构稳定性理论原理.唐家祥译.甘肃人民出版社, 1982: 71-103
6 Loannis G. Raftoyiannis, John Ch. Ermopoulos. Stability of Tapered and Stepped Steel Columns with Initial Imperfections. Engineering Structures. 2005, 27(8): 1248-1257
7 W.F. Chen. Structural Stability: From Theory to Practice. Engineering Structures. 2000, 22(2): 116-122
8刘光栋,罗汉泉.杆系结构稳定.人民交通出版社, 1988: 1-4
9楚中毅,陆念力,车仁炜,楚兰英.一种梁杆结构稳定性分析的精确有限元法.哈尔滨建筑大学学报, 2002, 35(4): 25-28
10李以申,陆念力,顾迪民.塔式起重机起重臂结构稳定计算的研究(三)——微分方程法求解阶梯状变截面非保向力悬臂梁构件的失稳临界力.建筑机械, 1997(1): 12-19
11李以申,陆念力,顾迪民.塔式起重机起重臂结构稳定计算的研究(一)——验算公式的使用和说明.建筑机械, 1996(12): 23-26
12张连文,郭卫军,王昊,马新敏,张忠海,陈以田,刘振.双吊点臂架整体稳定性校核段的选择.建筑机械化, 2003(2): 28-29
13李涵,塔式起重机双吊点水平臂整体稳定性分析研究.哈尔滨工业大学硕士学位论文. 2005: 29-36
14 GB 3811-83,起重机设计规范: 56-60
15 N.S. Trahair. Torsion, Bending and Buckling of Steel Beams. Engineering Structures. 1997, 19(5): 372-377
16 Lan Peng, Liu Manlan, Lu Nianli. Out-of-plane stability of a bending beam. GongchengLixue, 2005, 22: 152-155
17王佳,具有主副臂结构的起重机格构式臂架整体稳定性研究.哈尔滨工业大学硕士学位论文. 2006: 17-22
18薛渊.塔式起重机塔身刚度计算分析的高效方法.哈尔滨工业大学硕士学位论文. 2001: 25-30
19任体旺.格构式轴压构件稳定性计算及精度分析.哈尔滨工业大学硕士毕业论文. 2004: 35-52
20郑惠强.变截面悬臂构件顶端水平位移的简便计算.工程机械, 1992(7):21-23
21 O.C. Zienkiewicz, R.L. Taylor. The Finite Element Method. 5th Edi. Butterwort-Heinemann. 2000: 1-17
22 Klaus-Jürgen Bathe. Advances in Nonlinear Finite Element Analysis of Automobiles. 1997, 64(5): 881-891
23 Klaus-Jürgen Bathe. Finite Element procedures. Prentice Hall, Inc. 1996: 485-628
24蓝天,姚卓智.桅杆结构的非线形分析.中国建筑研究院结构所, 1980:2-4
25陆念力,兰朋,李良.二阶理论条件下的梁杆系统精确有限元方程及应用.哈尔滨建筑大学学报, 1998,31(4): 67-74
26陆念力,张立强,孟小平.梁杆系统精确有限元方程及其在几何非线性分析和稳定计算中的应用.建筑机械, 1996(3): 18-20
27陆念力.大位移梁杆非线性分析的一种使用方法. 1990(9):8-12
28陆念力,顾迪民.大位移杆系结构几何非线性分析与稳定性计算的有限元方法.建筑机械, 1991(10):8-12
29 S.Shimizu, M.Nakano. Strength and Behavior of the Corner Zones in Steel Rigid Frame Columns with Shifted Beams. Journal of Constructional Steel Research. 2000, 53(2): 245-263
30 Potrc I, Sraml M. On the Numerical Analysis of the Contact Problems at Crane Machanisms. Zeitschrift fur Angewandte Mathematik and Mechanik, 2000, 80(suppl2): S491-S492
31陈玮璋.起重机金属结构.人民交通出版社, 1987, 11
32 Edited by Edwin H.Gaylord Jr Charles N.Gaylord Structural Engineering Handbook. Second Edition
33王勖成.有限单元法.清华大学出版社, 2003: 55-77
34胡永飞.塔身腹杆体系探讨.建筑机械, 1992(2): 20-22
35 Mayer.G.Krafte an Raumfachwerkern Torsionsbeanspruchung Van Fachwerkturmen mit rechtechigem Querschnitt and parallelen seiten.fh.23.1973.13
36 S.P.铁摩辛柯.弹性稳定理论(第二版).科学出版社, 1965
37 Sung-Bo Kim, Moon-Young Kim. Improved formulation for spatial stability and free vibration of thin-walled tapered beams and space frames [J]. Engineering Structures. 2000, 22 (5): 446-458
38 Kiyohiro Imai, Dan M. Frangopol. Geometrically Nonlinear Finite Element Reliability Analysis of Structural Systems. Computers and Structures. 2000, 77(6): 677-691
39张质文,虞和谦,王金诺等.起重机设计手册.北京:中国铁道出版社, 1998
40李以申,陆念力,顾迪民.塔式起重机起重臂结构稳定计算的研究(二)——具有连续变化截面桁架构件的失稳临界力计算.建筑机械, 1996(12): 23-26
41李以申,陆念力,顾迪民.塔式起重机起重臂结构稳定计算的研究(四)——转角位移方程法求解构件失稳临界力.建筑机械, 1997(2): 9-13
42尹刚,冯贤桂.变截面压杆的临界压力近似计算.重庆工学院学报. 2005(11):22-24
43 Hasan ?ztürk, Mustafa Sabuncu. Stability analysis of a cantilever composite beam on elastic supports. Composites Science and Technology. 2005(65): 1982–1995
44陆念力,张立强.梁杆系统临界屈曲精确有限元判式及其应用.建筑机械化, 1996, (6): 8-10
45陆念力,兰朋,白桦.起重机箱形伸缩臂稳定性分析的精确理论解,哈尔滨建筑大学学报, 2000, 35(2): 89-93